Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 22RE
In Exercises 22–23, find a formula for the derivative of the function algebraically.
f(x) = 5x2 + x
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In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16
Each of Exercises 25–36 gives a formula for a function y = f(x). In
each case, find f-x) and identify the domain and range of f-. As a
check, show that f(fx)) = f-"f(x)) = x.
25. f(x) = x
26. f(x) = x, x20
%3D
%3D
27. f(x) = x + 1
28. f(x) = (1/2)x – 7/2
30. f(x) = 1/r, x * 0
%3D
29. f(x) = 1/x, x>0
x + 3
31. f(x)
32. f(x) =
VE - 3
34. f(x) = (2x + 1)/5
2
33. f(x) = x - 2r, xs1
(Hint: Complete the square.)
* + b
x - 2'
35. f(x) =
b>-2 and constant
36. f(x) = x?
2bx, b> 0 and constant, xsb
Chapter 2 Solutions
Calculus: Single And Multivariable
Ch. 2.1 - The distance, s, a car has traveled on a trip is...Ch. 2.1 - The table gives the position of a particle moving...Ch. 2.1 - The table gives the position of a particle moving...Ch. 2.1 - Figure 2.6 shows a particles distance from a point...Ch. 2.1 - Figure 2.7 shows a particles distance from a point...Ch. 2.1 - An observer tracks the distance a plane has rolled...Ch. 2.1 - At time t in seconds, a particles distance s(t),...Ch. 2.1 - At time t in seconds, a particles distance s(t),...Ch. 2.1 - In a time of t seconds, a particle moves a...Ch. 2.1 - In a time of t seconds, a particle moves a...
Ch. 2.1 - In a time of t seconds, a particle moves a...Ch. 2.1 - A car is driven at a constant speed. Sketch a...Ch. 2.1 - A car is driven at an increasing speed. Sketch a...Ch. 2.1 - A car starts at a high speed, and its speed then...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - In Problems 1520, estimate the limit by...Ch. 2.1 - Match the points labeled on the curve in Figure...Ch. 2.1 - For the function shown in Figure 2.10, at what...Ch. 2.1 - For the graph y = f(x) in Figure 2.11, arrange the...Ch. 2.1 - The graph of f(t) in Figure 2.12 gives the...Ch. 2.1 - Find the average velocity over the interval 0t0.2,...Ch. 2.1 - Figure 2.13 shows f(t) and g(t), the positions of...Ch. 2.1 - Prob. 27ECh. 2.1 - A particle moves along a line with varying...Ch. 2.1 - A ball is tossed into the air from a bridge, and...Ch. 2.1 - In Problems 3033, use algebra to evaluate the...Ch. 2.1 - In Problems 3033, use algebra to evaluate the...Ch. 2.1 - In Problems 3033, use algebra to evaluate the...Ch. 2.1 - In Problems 3033, use algebra to evaluate the...Ch. 2.1 - In Problems 3436, explain what is wrong with the...Ch. 2.1 - In Problems 3436, explain what is wrong with the...Ch. 2.1 - In Problems 3436, explain what is wrong with the...Ch. 2.1 - In Problems 3738, give an example of: A function...Ch. 2.1 - In Problems 3738, give an example of: A function...Ch. 2.1 - Are the statements in Problems 3943 true or false?...Ch. 2.1 - Are the statements in Problems 3943 true or false?...Ch. 2.1 - Are the statements in Problems 3943 true or false?...Ch. 2.1 - Are the statements in Problems 3943 true or false?...Ch. 2.1 - Are the statements in Problems 3943 true or false?...Ch. 2.2 - The table shows values of f(x) = x3 near x = 2 (to...Ch. 2.2 - By choosing small values for h, estimate the...Ch. 2.2 - The income that a company receives from selling an...Ch. 2.2 - (a) Make a table of values rounded to two decimal...Ch. 2.2 - (a) Make a table of values, rounded to two decimal...Ch. 2.2 - If f(x) = x3 + 4x, estimate f(3) using a table...Ch. 2.2 - Graph f(x) = sin x, and use the graph to decide...Ch. 2.2 - For the function f(x) = log x, estimate f(1). From...Ch. 2.2 - Estimate f(2) for f(x) = 3x. Explain your...Ch. 2.2 - The graph of y = f(x) is shown in Figure 2.21....Ch. 2.2 - Use Figure 2.22 to decide which is larger in each...Ch. 2.2 - Figure 2.23 shows the graph of f. Match the...Ch. 2.2 - Label points A, B, C, D, E, and F on the graph of...Ch. 2.2 - In Exercises 1418, interpret the expression in...Ch. 2.2 - In Exercises 1418, interpret the expression in...Ch. 2.2 - In Exercises 1418, interpret the expression in...Ch. 2.2 - In Exercises 1418, interpret the expression in...Ch. 2.2 - In Exercises 1418, interpret the expression in...Ch. 2.2 - Suppose that f(x) is a function with f(100) = 35...Ch. 2.2 - Show how to represent the following on Figure...Ch. 2.2 - For each of the following pairs of numbers, use...Ch. 2.2 - With the function f given by Figure 2.25, arrange...Ch. 2.2 - The function in Figure 2.26 has f(4) = 25 and...Ch. 2.2 - Use Figure 2.27 to fill in the blanks in the...Ch. 2.2 - On a copy of Figure 2.28, mark lengths that...Ch. 2.2 - On a copy of Figure 2.29, mark lengths that...Ch. 2.2 - Consider the function shown in Figure 2.30. (a)...Ch. 2.2 - (a) If f is even and f(10)=6, what is f(10)? (b)...Ch. 2.2 - If g is an odd function and g(4)=5, what is g(4)?Ch. 2.2 - (a) Estimate f(0) if f(x) = sin x, with x in...Ch. 2.2 - Find the equation of the tangent line to f(x) = x2...Ch. 2.2 - Estimate the instantaneous rate of change of the...Ch. 2.2 - Estimate the derivative of f(x) = xx at x = 2.Ch. 2.2 - For y = f(x) = 3x32 x, use your calculator to...Ch. 2.2 - Let f(x) = ln(cos x). Use your calculator to...Ch. 2.2 - The population, P(t), of China, in billions, can...Ch. 2.2 - The US population5 officially reached 300 million...Ch. 2.2 - For Problems 3841, estimate the change in y for...Ch. 2.2 - For Problems 3841, estimate the change in y for...Ch. 2.2 - For Problems 3841, estimate the change in y for...Ch. 2.2 - For Problems 3841, estimate the change in y for...Ch. 2.2 - (a) Graph f(x)=12x2 and g(x) = f(x) + 3 on the...Ch. 2.2 - Suppose Table 2.3 on page 94 is continued with...Ch. 2.2 - (a) Let f(x) = x2. Explain what Table 2.5 tells us...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - Use algebra to evaluate the limits in Problems...Ch. 2.2 - For Problems 5155, estimate the value of f(1) by...Ch. 2.2 - For Problems 5155, estimate the value of f(1) by...Ch. 2.2 - For Problems 5155, estimate the value of f(1) by...Ch. 2.2 - For Problems 5155, estimate the value of f(1) by...Ch. 2.2 - For Problems 5155, estimate the value of f(1) by...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - Find the derivatives in Problems 5661...Ch. 2.2 - For Problems 6265, find the equation of the line...Ch. 2.2 - For Problems 6265, find the equation of the line...Ch. 2.2 - For Problems 6265, find the equation of the line...Ch. 2.2 - For Problems 6265, find the equation of the line...Ch. 2.2 - In Problems 6667, explain what is wrong with the...Ch. 2.2 - In Problems 6667, explain what is wrong with the...Ch. 2.2 - In Problems 6869, give an example of: A continuous...Ch. 2.2 - In Problems 6869, give an example of: A linear...Ch. 2.2 - Are the statements in Problems 7072 true or false?...Ch. 2.2 - Are the statements in Problems 7072 true or false?...Ch. 2.2 - Are the statements in Problems 7072 true or false?...Ch. 2.2 - Assume that f is an odd function and that f(2)=3,...Ch. 2.3 - (a) Estimate f(2) using the values of f in the...Ch. 2.3 - Find approximate values for f(x) at each of the...Ch. 2.3 - Values of f(x) are in the table. Where in the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 413, graph the derivative of the...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - For Exercises 1419, sketch the graph of f(x), and...Ch. 2.3 - In Exercises 2021, find a formula for the...Ch. 2.3 - In Exercises 2021, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In Exercises 2227, find a formula for the...Ch. 2.3 - In each case, graph a smooth curve whose slope...Ch. 2.3 - Draw a possible graph of y = f(x) given the...Ch. 2.3 - For f(x) = ln x, construct tables, rounded to four...Ch. 2.3 - Given the numerical values shown, find approximate...Ch. 2.3 - Values of x and g(x) are given in the table. For...Ch. 2.3 - In the graph of f in Figure 2.35, at which of the...Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - For Problems 3443, sketch the graph of f(x).Ch. 2.3 - In Problems 4447, match f with the corresponding f...Ch. 2.3 - In Problems 4447, match f with the corresponding f...Ch. 2.3 - In Problems 4447, match f with the corresponding f...Ch. 2.3 - In Problems 4447, match f with the corresponding f...Ch. 2.3 - Roughly sketch the shape of the graph of a...Ch. 2.3 - A vehicle moving along a straight road has...Ch. 2.3 - A child inflates a balloon, admires it for a while...Ch. 2.3 - Figure 2.39 shows a graph of voltage across an...Ch. 2.3 - Figure 2.40 is the graph of f, the derivative of a...Ch. 2.3 - The derivative of f is the spike function in...Ch. 2.3 - The population of a herd of deer is modeled by...Ch. 2.3 - The graph in Figure 2.42 shows the accumulated...Ch. 2.3 - Draw the graph of a continuous function y = f(x)...Ch. 2.3 - Prob. 57ECh. 2.3 - If limxf(x)=50 and f(x) is positive for all x,...Ch. 2.3 - Using a graph, explain why if f(x) is an even...Ch. 2.3 - Using a graph, explain why if g(x) is an odd...Ch. 2.3 - In Problems 6163, explain what is wrong with the...Ch. 2.3 - In Problems 6163, explain what is wrong with the...Ch. 2.3 - In Problems 6163, explain what is wrong with the...Ch. 2.3 - In Problems 6465, give an example of: A function...Ch. 2.3 - In Problems 6465, give an example of: A family of...Ch. 2.3 - Are the statements in Problems 6669 true or false?...Ch. 2.3 - Are the statements in Problems 6669 true or false?...Ch. 2.3 - Are the statements in Problems 6669 true or false?...Ch. 2.3 - Are the statements in Problems 6669 true or false?...Ch. 2.4 - The cost, C (in dollars), to produce g gallons of...Ch. 2.4 - The time for a chemical reaction, T (in minutes),...Ch. 2.4 - The temperature, T, in degrees Fahrenheit, of a...Ch. 2.4 - The temperature, H, in degrees Celsius, of a cup...Ch. 2.4 - The cost, C (in dollars), to produce q quarts of...Ch. 2.4 - An economist is interested in how the price of a...Ch. 2.4 - Let S(t) be the amount of water, measured in...Ch. 2.4 - The wind speed, W, in meters per second, at a...Ch. 2.4 - Suppose C(r) is the total cost of paying off a car...Ch. 2.4 - Let f(x) be the elevation in feet of the...Ch. 2.4 - In Exercises 1115, give the units and sign of the...Ch. 2.4 - In Exercises 1115, give the units and sign of the...Ch. 2.4 - In Exercises 1115, give the units and sign of the...Ch. 2.4 - In Exercises 1115, give the units and sign of the...Ch. 2.4 - In Exercises 1115, give the units and sign of the...Ch. 2.4 - Suppose P(t) is the monthly payment, in dollars,...Ch. 2.4 - After investing 1000 at an annual interest rate of...Ch. 2.4 - Investing 1000 at an annual interest rate of r%,...Ch. 2.4 - Meteorologists define the temperature lapse rate...Ch. 2.4 - Let dVdrr=2=16. (a) For small r, write an...Ch. 2.4 - Let R = f(S) and f(10)=3. (a) For small S, write...Ch. 2.4 - Let y = f(x) with f(3) = 5 and f(3)=9. (a) For...Ch. 2.4 - If t is the number of years since 2014, the...Ch. 2.4 - A city grew in population throughout the 1980s and...Ch. 2.4 - Prob. 25ECh. 2.4 - Analysis of satellite data indicates that the...Ch. 2.4 - A laboratory study investigating the relationship...Ch. 2.4 - An economist is interested in how the price of a...Ch. 2.4 - On May 9, 2007, CBS Evening News had a 4.3 point...Ch. 2.4 - Let W(h) be an invertible function which tells how...Ch. 2.4 - The population of Mexico in millions is P = f(t),...Ch. 2.4 - Let f(t) be the number of centimeters of rainfall...Ch. 2.4 - Water is flowing into a tank; the depth, in feet,...Ch. 2.4 - As the altitude of an object increases, the...Ch. 2.4 - As the distance of an object from the surface of...Ch. 2.4 - The acceleration a, in meters/second2, of a child...Ch. 2.4 - Let p(h) be the pressure in dynes per cm2 on a...Ch. 2.4 - Let g(t)be the height, in inches, of Amelia...Ch. 2.4 - If g(v) is the fuel efficiency, in miles per...Ch. 2.4 - The function P(d) gives the total electricity, in...Ch. 2.4 - Let P be the total petroleum reservoir on Earth in...Ch. 2.4 - (a) If you jump out of an airplane without a...Ch. 2.4 - Let W be the amount of water, in gallons, in a...Ch. 2.4 - The temperature T of the atmosphere depends on the...Ch. 2.4 - The Arctic Sea ice extent, the area of sea covered...Ch. 2.4 - The depth, h (in mm), of the water runoff down a...Ch. 2.4 - Average leaf width, w (in mm), in tropical...Ch. 2.4 - When an ice dam for a glacial lake breaks, the...Ch. 2.4 - The growth rate, R(in cell divisions per hour), of...Ch. 2.4 - A companys revenue from car sales, C (in thousands...Ch. 2.4 - In April 2015 in the US, there was one birth every...Ch. 2.4 - Prob. 52ECh. 2.4 - Let P(x) be the number of people of height x...Ch. 2.4 - When you breathe, a muscle (called the diaphragm)...Ch. 2.4 - In Problems 5557, explain what is wrong with the...Ch. 2.4 - In Problems 5557, explain what is wrong with the...Ch. 2.4 - In Problems 5557, explain what is wrong with the...Ch. 2.4 - In Problems 5859, give an example of: A function...Ch. 2.4 - In Problems 5859, give an example of: A function...Ch. 2.4 - Are the statements in Problems 6063 true or false?...Ch. 2.4 - Are the statements in Problems 6063 true or false?...Ch. 2.4 - Are the statements in Problems 6063 true or false?...Ch. 2.4 - Are the statements in Problems 6063 true or false?...Ch. 2.4 - For Problems 6465, assume g(v) is the fuel...Ch. 2.4 - For Problems 6465, assume g(v) is the fuel...Ch. 2.5 - Fill in the blanks: (a) If f is positive on an...Ch. 2.5 - For the function graphed in Figure 2.52, are the...Ch. 2.5 - At one of the labeled points on the graph in...Ch. 2.5 - At exactly two of the labeled points in Figure...Ch. 2.5 - Graph the functions described in parts (a)(d). (a)...Ch. 2.5 - Sketch the graph of a function whose first...Ch. 2.5 - Sketch the graph of the height of a particle...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - For Exercises 813, give the signs of the first and...Ch. 2.5 - The position of a particle moving along the x-axis...Ch. 2.5 - The table gives the number of passenger cars, C =...Ch. 2.5 - An accelerating sports car goes from 0 mph to 60...Ch. 2.5 - A small plane is taking off from a runway at a...Ch. 2.5 - Sketch the curves described in (a)(c): (a) Slope...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - In Problems 1924, graph the second derivative of...Ch. 2.5 - Let P(t) represent the price of a share of stock...Ch. 2.5 - A headline in the New York Times on December 14,...Ch. 2.5 - In economics, total utility refers to the total...Ch. 2.5 - Winning the war on poverty has been described...Ch. 2.5 - An industry is being charged by the Environmental...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - In Problems 3035, the length of a plant, L, is a...Ch. 2.5 - At which of the marked x-values in Figure 2.56 can...Ch. 2.5 - Figure 2.57 gives the position, f(t), of a...Ch. 2.5 - The graph of f (not f) is given in Figure 2.58. At...Ch. 2.5 - For Problems 3940, sketch the graph of one...Ch. 2.5 - For Problems 3940, sketch the graph of one...Ch. 2.5 - A function f has f(5) = 20, f(5)=2, and f(x)0, for...Ch. 2.5 - Chlorofluorocarbons (CFCs) were used as...Ch. 2.5 - (a) Using the graph of f in Figure 2.59, for what...Ch. 2.5 - In Problems 4445, explain what is wrong with the...Ch. 2.5 - In Problems 4445, explain what is wrong with the...Ch. 2.5 - In Problems 4647, give an example of: A function...Ch. 2.5 - In Problems 4647, give an example of: A function...Ch. 2.5 - Are the statements in Problems 4852 true or false?...Ch. 2.5 - Are the statements in Problems 4852 true or false?...Ch. 2.5 - Are the statements in Problems 4852 true or false?...Ch. 2.5 - Are the statements in Problems 4852 true or false?...Ch. 2.5 - Are the statements in Problems 4852 true or false?...Ch. 2.6 - For the graphs in Exercises 12, list the x-values...Ch. 2.6 - For the graphs in Exercises 12, list the x-values...Ch. 2.6 - In Exercises 34, does the function appear to be...Ch. 2.6 - In Exercises 34, does the function appear to be...Ch. 2.6 - In Exercises 57, decide if the function is...Ch. 2.6 - In Exercises 57, decide if the function is...Ch. 2.6 - In Exercises 57, decide if the function is...Ch. 2.6 - Decide if the functions in Problems 810 are...Ch. 2.6 - Decide if the functions in Problems 810 are...Ch. 2.6 - Decide if the functions in Problems 810 are...Ch. 2.6 - In each of the following cases, sketch the graph...Ch. 2.6 - Look at the graph of f(x) = (x2 + 0.0001)12 shown...Ch. 2.6 - The acceleration due to gravity, g, varies with...Ch. 2.6 - An electric charge, Q, in a circuit is given as a...Ch. 2.6 - A magnetic field, B, is given as a function of the...Ch. 2.6 - Prob. 16ECh. 2.6 - Graph the function defined by...Ch. 2.6 - The potential, , of a charge distribution at a...Ch. 2.6 - Sometimes, odd behavior can be hidden beneath the...Ch. 2.6 - Figure 2.65 shows graphs of four useful but non...Ch. 2.6 - In Problems 2122, explain what is wrong with the...Ch. 2.6 - In Problems 2122, explain what is wrong with the...Ch. 2.6 - In Problems 2325, give an example of: A continuous...Ch. 2.6 - In Problems 2325, give an example of: An...Ch. 2.6 - In Problems 2325, give an example of: A rational...Ch. 2.6 - Are the statements in Problems 2630 true or false?...Ch. 2.6 - Are the statements in Problems 2630 true or false?...Ch. 2.6 - Are the statements in Problems 2630 true or false?...Ch. 2.6 - Are the statements in Problems 2630 true or false?...Ch. 2.6 - Are the statements in Problems 2630 true or false?...Ch. 2.6 - Which of the following would be a counterexample...Ch. 2 - At time t in seconds, a particles distance s(t),...Ch. 2 - Prob. 2RECh. 2 - In Exercises 27, find the average velocity for the...Ch. 2 - In Exercises 27, find the average velocity for the...Ch. 2 - In Exercises 27, find the average velocity for the...Ch. 2 - In Exercises 27, find the average velocity for the...Ch. 2 - In Exercises 27, find the average velocity for the...Ch. 2 - In a time of t seconds, a particle moves a...Ch. 2 - A bicyclist pedals at a fairly constant rate, with...Ch. 2 - As you drive away from home, your speed is fast,...Ch. 2 - (a) Graph f(x) = x sin x for 10 x 10. (b) How...Ch. 2 - (a) Using the data in the table, estimate an...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Sketch the graphs of the derivatives of the...Ch. 2 - Roughly sketch the shape of the graph of a cubic...Ch. 2 - In Exercises 2021, graph the second derivative of...Ch. 2 - In Exercises 2021, graph the second derivative of...Ch. 2 - In Exercises 2223, find a formula for the...Ch. 2 - In Exercises 2223, find a formula for the...Ch. 2 - Find the derivative of f(x) = x2 + 1 at x = 3...Ch. 2 - (a) Between which pair of consecutive points in...Ch. 2 - In Exercises 2630, use the difference quotient...Ch. 2 - In Exercises 2630, use the difference quotient...Ch. 2 - In Exercises 2630, use the difference quotient...Ch. 2 - In Exercises 2630, use the difference quotient...Ch. 2 - In Exercises 2630, use the difference quotient...Ch. 2 - In Exercises 3135, evaluate the limit...Ch. 2 - In Exercises 3135, evaluate the limit...Ch. 2 - In Exercises 3135, evaluate the limit...Ch. 2 - In Exercises 3135, evaluate the limit...Ch. 2 - In Exercises 3135, evaluate the limit...Ch. 2 - Sketch the graph of a function whose first and...Ch. 2 - Figure 2.2 gives the position, y = s(t), of a...Ch. 2 - Match each property (a)(d) with one or more of...Ch. 2 - (a) In Figure 2.3, if f(t) gives the position of a...Ch. 2 - The table1 gives the number of passenger cars, C =...Ch. 2 - Let f(t) be the depth, in centimeters, of water in...Ch. 2 - If t is the number of years since 2010, the...Ch. 2 - The revenue, in thousands of dollars, earned by a...Ch. 2 - (a) Give an example of a function with limx2f(x)=....Ch. 2 - Draw a possible graph of y = f(x) given the...Ch. 2 - Suppose f(2) = 3 and f(2)=1. Find f(2) and f(2),...Ch. 2 - Do the values for the function y = k(x) in the...Ch. 2 - Suppose that f(x) is a function with f(20) = 345...Ch. 2 - Students were asked to evaluate f(4) from the...Ch. 2 - Use Figure 2.4 to fill in the blanks in the...Ch. 2 - Use Figure 2.5. At point A, we are told that x =...Ch. 2 - Given all of the following information about a...Ch. 2 - Suppose w is the weight of a stack of papers in an...Ch. 2 - A yam has just been taken out of the oven and is...Ch. 2 - For some painkillers, the size of the dose, D,...Ch. 2 - In April 1991, the Economist carried an article3...Ch. 2 - At time, t, in years, the US population is growing...Ch. 2 - A continuous function defined for all x has the...Ch. 2 - (a) Using the table, estimate f(0.6) and f(0.5)....Ch. 2 - Let g(x)=x and f(x) = kx2, where k is a constant....Ch. 2 - A circle with center at the origin and radius of...Ch. 2 - Each of the graphs in Figure 2.6 shows the...Ch. 2 - The population of a herd of deer is modeled by...Ch. 2 - The number of hours, H, of daylight in Madrid is a...Ch. 2 - You put a yam in a hot oven, maintained at a...Ch. 2 - You are given the following values for the error...Ch. 2 - (a) Use your calculator to approximate the...Ch. 2 - In 2009, a study was done on the impact of...
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- In Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5arrow_forwardIn Exercises 22–27, find a formula for the derivative of the function using the difference quotient. 22. g(x)= 2x² – 3 23. m(x) = 1/(x + 1)arrow_forwardIn Exercises 87–88, use the graph of f(x) = |4 – x| to solve each equation or inequality. y flx) = |4 – x| y = 53- y = 1 $ 9 10 87. 14 - x| = 1 88. 14 - x| < 5arrow_forward
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- Find the fifth derivative of (2x+3)5arrow_forward3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d %3D dx |x| b) Sketch the graphs of the function f(x) = |x| and its derivative. %3D c) Use the result of part (a) to differentiate the function g(x) = x|x|. Write the derivative as a simplified monomial. %3Darrow_forwardDraw the graph of any function f (x) that passes through the point (3, 2).arrow_forward
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Derivatives of Trigonometric Functions - Product Rule Quotient & Chain Rule - Calculus Tutorial; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=_niP0JaOgHY;License: Standard YouTube License, CC-BY