Calculus (MindTap Course List)
Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Chapter 3.7, Problem 46E

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v 3 . It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u ( u < v ) , then the time required to swim a distance L is L / ( v − u ) and the total energy E required to swim the distance is given by

where a is the proportionality constant.

(a) Determine the value of v that minimizes E.

(b) Sketch the graph of E.

Note: This result has been verified experimentally; migrating fish swim against a current at a speed 50% greater than the current speed.

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Chapter 3 Solutions

Calculus (MindTap Course List)

Ch. 3.1 - Explain the difference between an absolute minimum...Ch. 3.1 - Suppose f is a continuous function defined on a...Ch. 3.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 3.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 3.1 - Use the graph to state the absolute and local...Ch. 3.1 - Use the graph to state the absolute and local...Ch. 3.1 - Sketch the graph of a function f that is...Ch. 3.1 - Sketch the graph of a function f that is...Ch. 3.1 - Prob. 9ECh. 3.1 - Sketch the graph of a function f that is...
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - a Sketch the graph of a function on [1,2] that has...Ch. 3.1 - Prob. 14ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 24ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Find the critical numbers of the function....Ch. 3.1 - Prob. 36ECh. 3.1 - Find the critical numbers of the function....Ch. 3.1 - Prob. 38ECh. 3.1 - Find the critical numbers of the function....Ch. 3.1 - Prob. 40ECh. 3.1 - Find the critical numbers of the function....Ch. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Find the absolute maximum and absolute minimum...Ch. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Find the absolute maximum and absolute minimum...Ch. 3.1 - Prob. 52ECh. 3.1 - Find the absolute maximum and absolute minimum...Ch. 3.1 - Prob. 54ECh. 3.1 - Find the absolute maximum and absolute minimum...Ch. 3.1 - Prob. 56ECh. 3.1 - If a and b are positive numbers, find the maximum...Ch. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - An object with weight W is dragged along a...Ch. 3.1 - The water level, measured in feet above mean sea...Ch. 3.1 - On May 7, 1992, the space shuttle Endeavour was...Ch. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prove that the function f(x)=x101+x51+x+1 has...Ch. 3.1 - If f has a local minimum value at c, show that the...Ch. 3.1 - Prove Fermats Theorem for the case in which f has...Ch. 3.1 - Prob. 72ECh. 3.2 - The graph of a function f is shown. Verify that f...Ch. 3.2 - Draw the graph of a function defined on 0, 8 such...Ch. 3.2 - The graph of a function g is shown. a Verify that...Ch. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - 5-8 Verify that the function satisfies the three...Ch. 3.2 - Prob. 8ECh. 3.2 - Let f(x)=1x2/3. Show that f(1)=f(1) but there is...Ch. 3.2 - Let f(x)=tanx. Show that f(0)=f() but there is no...Ch. 3.2 - 11-14 Verify that the function satisfies the...Ch. 3.2 - Prob. 12ECh. 3.2 - 11-14 Verify that the function satisfies the...Ch. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - 15-16 Find the number c that satisfies the...Ch. 3.2 - Let f(x)=(x3)2. Show that there is no value of c...Ch. 3.2 - Let f(x)=2|2x1|. Show that there is no value of c...Ch. 3.2 - 19-20 Show that the equation has exactly one real...Ch. 3.2 - Prob. 20ECh. 3.2 - Show that the equation x315x+c=0 has at most one...Ch. 3.2 - Show that the equation x4+4x+c=0 has at most two...Ch. 3.2 - a Show that a polynomial of degree 3 has at most...Ch. 3.2 - Prob. 24ECh. 3.2 - If f(1)=10 and f(x)2 for 1x4, how small can f(4)...Ch. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Suppose that f and g are continuous on a, b and...Ch. 3.2 - Prob. 29ECh. 3.2 - Suppose f is an odd function and is differentiable...Ch. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - At 2:00 pm a cars speedometer reads 30 mi/h. At...Ch. 3.2 - Two runners start a race at the same time and...Ch. 3.2 - A number a is called a fixed point of a function f...Ch. 3.3 - 1-2 Use the given graph of f to find the...Ch. 3.3 - 1-2 Use the given graph of f to find the...Ch. 3.3 - Suppose you are given a formula for a function f....Ch. 3.3 - a State the First Derivative Test. b State the...Ch. 3.3 - 5-6 The graph of the derivative f of a function f...Ch. 3.3 - 5-6 The graph of the derivative f of a function f...Ch. 3.3 - In each part state the x-coordinates of the...Ch. 3.3 - The graph of the first derivative f of a function...Ch. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - 9-14 a Find the intervals on which f is increasing...Ch. 3.3 - Prob. 14ECh. 3.3 - 15-17 Find the local maximum and minimum values of...Ch. 3.3 - Prob. 16ECh. 3.3 - 15-17 Find the local maximum and minimum values of...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - 20-27 Sketch the graph of a function that...Ch. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Suppose f is a continuous function where f(x)0 for...Ch. 3.3 - The graph of a function y=f(x) is shown. At which...Ch. 3.3 - 31-32 The graph of the derivative f of a...Ch. 3.3 - 31-32 The graph of the derivative f of a...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - 33-44 a Find the intervals of increase or...Ch. 3.3 - 33-44 a Find the intervals of increase or...Ch. 3.3 - Prob. 38ECh. 3.3 - 33-44 a Find the intervals of increase or...Ch. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - 33-44 a Find the intervals of increase or...Ch. 3.3 - 33-44 a Find the intervals of increase or...Ch. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - 47-48 a Use a graph of f to estimate the maximum...Ch. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - A graph of a population of yeast cells in a new...Ch. 3.3 - In an episode of The Simpsons television show,...Ch. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - a If the function f(x)=x3+ax2+bx has the local...Ch. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Show that a cubic function a third-degree...Ch. 3.3 - For what values of c does the polynomial...Ch. 3.3 - Prove that if (c,f(c)) is a point of inflection of...Ch. 3.3 - Show that if f(x)=x4, then f(0)=0, but 0, 0 is not...Ch. 3.3 - Show that the function g(x)=x|x| has an inflection...Ch. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - The three cases in the First Derivative Test cover...Ch. 3.4 - Explain in your own words the meaning of each of...Ch. 3.4 - a Can the graph of y=f(x) intersect a vertical...Ch. 3.4 - For the function f whose graph is given, state the...Ch. 3.4 - For the function g whose graph is given, state the...Ch. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - 7-8 Evaluate the limit and justify each step by...Ch. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - 9-32 Find the limit or show that it does not...Ch. 3.4 - a Estimate the value of limx(x2+x+1+x) by graphing...Ch. 3.4 - a Use a graph of f(x)=3x2+8x+63x2+3x+1 to estimate...Ch. 3.4 - 35-40 Find the horizontal and vertical asymptotes...Ch. 3.4 - 35-40 Find the horizontal and vertical asymptotes...Ch. 3.4 - 35-40 Find the horizontal and vertical asymptotes...Ch. 3.4 - 35-40 Find the horizontal and vertical asymptotes...Ch. 3.4 - 35-40 Find the horizontal and vertical asymptotes...Ch. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Let P and Q be polynomials. Find limxP(x)Q(x) if...Ch. 3.4 - Prob. 44ECh. 3.4 - Find a formula for a function / that satisfies the...Ch. 3.4 - Prob. 46ECh. 3.4 - A function f is a ratio of quadratic functions and...Ch. 3.4 - Prob. 48ECh. 3.4 - 48-51 Find the horizontal asymptotes of the curve...Ch. 3.4 - 48-51 Find the horizontal asymptotes of the curve...Ch. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - 57-60 Sketch the graph of a function that...Ch. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - a Use the Squeeze Theorem to evaluate limxsinxx. b...Ch. 3.4 - By the end behavior of a function we mean the...Ch. 3.4 - Prob. 63ECh. 3.4 - a A tank contains 5000 L of pure water. Brine that...Ch. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - For the limit limx13xx2+1=3 illustrate Definition...Ch. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 2ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 4ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 6ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 12ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 14ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 16ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 18ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - 1-40 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - The figure shows a beam of length L embedded in...Ch. 3.5 - Coulombs Law states that the force of attraction...Ch. 3.5 - 4548 Find an equation of the slant asymptote. Do...Ch. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - 4954 Use the guidelines of this section to sketch...Ch. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Use the asymptotic behavior of f(x)=cosx+1/x2 to...Ch. 3.6 - 18 Produce graphs of f that reveal all the...Ch. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.7 - Consider the following problem: Find two numbers...Ch. 3.7 - Find two numbers whose difference is 100 and whose...Ch. 3.7 - Find two positive numbers whose product is 100 and...Ch. 3.7 - The sum of two positive numbers is 16. What is the...Ch. 3.7 - What is the maximum vertical distance between the...Ch. 3.7 - Prob. 6ECh. 3.7 - Find the dimensions of a rectangle with perimeter...Ch. 3.7 - Find the dimensions of a rectangle with area 1000...Ch. 3.7 - A model used for the yield y of an agricultural...Ch. 3.7 - The rate in mg carbon/m3/h at which photosynthesis...Ch. 3.7 - Consider the following problem: A farmer with 750...Ch. 3.7 - Consider the following problem: A box with an open...Ch. 3.7 - A farmer wants to fence in an area of 1.5 million...Ch. 3.7 - Prob. 14ECh. 3.7 - If 1200 cm2 of material is available to make a box...Ch. 3.7 - Prob. 16ECh. 3.7 - Do Exercise 16 assuming the container has a fid...Ch. 3.7 - Prob. 18ECh. 3.7 - If the farmer in Exercise 18 wants to enclose 8000...Ch. 3.7 - a Show that of all the rectangles with a given...Ch. 3.7 - Find the point on the line y=2x+3 that is closest...Ch. 3.7 - Prob. 22ECh. 3.7 - Find the points on the ellipse 4x2+y2=4 that are...Ch. 3.7 - Find, correct to two decimal places, the...Ch. 3.7 - Find the dimensions of the rectangle of largest...Ch. 3.7 - Find the area of the largest rectangle that can be...Ch. 3.7 - Find the dimensions of the rectangle of largest...Ch. 3.7 - Find the area of the largest trapezoid that can be...Ch. 3.7 - Find the dimensions of the isosceles triangle of...Ch. 3.7 - If the two equal sides of an isosceles triangle...Ch. 3.7 - Prob. 31ECh. 3.7 - A right circular cylinder is inscribed in a cone...Ch. 3.7 - A right circular cylinder is inscribed in a sphere...Ch. 3.7 - A Norman window has the shape of a rectangle...Ch. 3.7 - Prob. 35ECh. 3.7 - A poster is to have an area of 180 in 2 with...Ch. 3.7 - A piece of wire 10 m long is cut into two pieces....Ch. 3.7 - Solve Exercise 37 if one piece is bent into a...Ch. 3.7 - If you are offered one slice from a round pizza in...Ch. 3.7 - Prob. 40ECh. 3.7 - Prob. 41ECh. 3.7 - A cone-shaped paper drinking cup is to be made to...Ch. 3.7 - A cone with height h is inscribed in a larger cone...Ch. 3.7 - Prob. 44ECh. 3.7 - Prob. 45ECh. 3.7 - For a fish swimming at a speed v relative to the...Ch. 3.7 - In a beehive, each cell is a regular hexagonal...Ch. 3.7 - A boat leaves a dock at 2:00 PM and travels due...Ch. 3.7 - Solve the problem in Example 4 if the river is 5...Ch. 3.7 - A woman at a point A on the shore of a circular...Ch. 3.7 - An oil refinery is located on the north bank of a...Ch. 3.7 - Suppose the refinery in Exercise 51 is located 1...Ch. 3.7 - Prob. 53ECh. 3.7 - Prob. 54ECh. 3.7 - Let a and b be positive numbers. Find the length...Ch. 3.7 - Prob. 56ECh. 3.7 - Prob. 57ECh. 3.7 - What is the smallest possible area of the triangle...Ch. 3.7 - Prob. 59ECh. 3.7 - Prob. 60ECh. 3.7 - Prob. 61ECh. 3.7 - During the summer months Terry makes and sells...Ch. 3.7 - A retailer has been selling 1200 tablet computers...Ch. 3.7 - A company operates 16 oil wells in a designated...Ch. 3.7 - Show that of all the isosceles triangles with a...Ch. 3.7 - Prob. 66ECh. 3.7 - Consider the tangent line to the ellipse...Ch. 3.7 - The frame for a kite is to be made from six pieces...Ch. 3.7 - A point P needs to be located somewhere on the...Ch. 3.7 - The graph shows the fuel consumption c of a car...Ch. 3.7 - Let v1 be the velocity of light in air and v2 the...Ch. 3.7 - Two vertical poles PQ and ST are secured by a rope...Ch. 3.7 - The upper right-hand corner of a piece of paper,...Ch. 3.7 - A steel pipe is being carried down a hallway 9 ft...Ch. 3.7 - An observer stands at a point P, one unit away...Ch. 3.7 - A rain gutter is to be constructed from a metal...Ch. 3.7 - Prob. 77ECh. 3.7 - The blood vascular system consists of blood...Ch. 3.7 - Ornithologists have determined that some species...Ch. 3.7 - Two light sources of identical strength are placed...Ch. 3.8 - The figure shows the graph of a function f....Ch. 3.8 - Prob. 2ECh. 3.8 - Suppose the tangent line to the curve y=f(x) at...Ch. 3.8 - For each initial approximation, determine...Ch. 3.8 - For which of the initial approximations x1=a,b,c,...Ch. 3.8 - Prob. 6ECh. 3.8 - Prob. 7ECh. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Prob. 11ECh. 3.8 - Prob. 12ECh. 3.8 - Prob. 13ECh. 3.8 - Prob. 14ECh. 3.8 - Prob. 15ECh. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Prob. 18ECh. 3.8 - Prob. 19ECh. 3.8 - Prob. 20ECh. 3.8 - Prob. 21ECh. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - Prob. 24ECh. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Explain why Newtons method doesnt work for finding...Ch. 3.8 - a Use Newtons method with x1=1 to find the root of...Ch. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - a Use Newtons method to find the critical numbers...Ch. 3.8 - Prob. 34ECh. 3.8 - Use Newtons method to find the coordinates of the...Ch. 3.8 - Prob. 36ECh. 3.8 - Use Newtons method to find the coordinates,...Ch. 3.8 - In the figure, the length of the chord AB is 4 cm...Ch. 3.8 - Prob. 39ECh. 3.8 - Prob. 40ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 2ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 4ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 6ECh. 3.9 - Prob. 7ECh. 3.9 - Prob. 8ECh. 3.9 - Prob. 9ECh. 3.9 - Prob. 10ECh. 3.9 - Prob. 11ECh. 3.9 - Prob. 12ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 14ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 16ECh. 3.9 - Prob. 17ECh. 3.9 - Prob. 18ECh. 3.9 - Prob. 19ECh. 3.9 - Prob. 20ECh. 3.9 - Prob. 21ECh. 3.9 - Prob. 22ECh. 3.9 - Prob. 23ECh. 3.9 - Prob. 24ECh. 3.9 - Prob. 25ECh. 3.9 - Prob. 26ECh. 3.9 - Prob. 27ECh. 3.9 - Prob. 28ECh. 3.9 - 23-42 Find f. f(x)=1+3x,f(4)=25Ch. 3.9 - Prob. 30ECh. 3.9 - 23-42 Find f. f(x)=x(6+5x),f(1)=10Ch. 3.9 - Prob. 32ECh. 3.9 - Prob. 33ECh. 3.9 - Prob. 34ECh. 3.9 - Prob. 35ECh. 3.9 - Prob. 36ECh. 3.9 - Prob. 37ECh. 3.9 - Prob. 38ECh. 3.9 - 23-42 Find f. f(x)=4+6x+24x2,f(0)=3,f(1)=10Ch. 3.9 - Prob. 40ECh. 3.9 - Prob. 41ECh. 3.9 - Prob. 42ECh. 3.9 - Prob. 43ECh. 3.9 - Prob. 44ECh. 3.9 - 45-46 The graph of a function f is shown. Which...Ch. 3.9 - 45-46 The graph of a function f is shown. Which...Ch. 3.9 - The graph of a function is shown in the figure....Ch. 3.9 - The graph of the velocity function of a particle...Ch. 3.9 - Prob. 49ECh. 3.9 - Prob. 50ECh. 3.9 - Prob. 51ECh. 3.9 - Prob. 52ECh. 3.9 - Prob. 53ECh. 3.9 - Prob. 54ECh. 3.9 - Prob. 55ECh. 3.9 - Prob. 56ECh. 3.9 - Prob. 57ECh. 3.9 - Prob. 58ECh. 3.9 - A stone is dropped from the upper observation deck...Ch. 3.9 - Show that for motion in a straight line with...Ch. 3.9 - An object is projected upward with initial...Ch. 3.9 - Prob. 62ECh. 3.9 - Prob. 63ECh. 3.9 - If a diver of mass m stands at the end of a diving...Ch. 3.9 - Prob. 65ECh. 3.9 - Prob. 66ECh. 3.9 - Since raindrops grow as they fall, their surface...Ch. 3.9 - Prob. 68ECh. 3.9 - Prob. 69ECh. 3.9 - Prob. 70ECh. 3.9 - Prob. 71ECh. 3.9 - A model rocket is fired vertically upward from...Ch. 3.9 - Prob. 73ECh. 3.R - Prob. 1CCCh. 3.R - Prob. 2CCCh. 3.R - a State Fermats Theorem. b Define a critical...Ch. 3.R - Prob. 4CCCh. 3.R - Prob. 5CCCh. 3.R - Prob. 6CCCh. 3.R - Prob. 7CCCh. 3.R - Prob. 8CCCh. 3.R - If you have a graphing calculator or computer, why...Ch. 3.R - Prob. 10CCCh. 3.R - Prob. 11CCCh. 3.R - Prob. 1TFQCh. 3.R - Prob. 2TFQCh. 3.R - Prob. 3TFQCh. 3.R - Prob. 4TFQCh. 3.R - Determine whether the statement is true or false....Ch. 3.R - Prob. 6TFQCh. 3.R - Prob. 7TFQCh. 3.R - Prob. 8TFQCh. 3.R - Prob. 9TFQCh. 3.R - Prob. 10TFQCh. 3.R - Prob. 11TFQCh. 3.R - Prob. 12TFQCh. 3.R - Prob. 13TFQCh. 3.R - Prob. 14TFQCh. 3.R - Prob. 15TFQCh. 3.R - Prob. 16TFQCh. 3.R - Prob. 17TFQCh. 3.R - Prob. 18TFQCh. 3.R - Prob. 19TFQCh. 3.R - Prob. 1ECh. 3.R - Prob. 2ECh. 3.R - 1-6 Find the local and absolute extreme values of...Ch. 3.R - Prob. 4ECh. 3.R - 1-6 Find the local and absolute extreme values of...Ch. 3.R - Prob. 6ECh. 3.R - Prob. 7ECh. 3.R - 7-12 Find the limit. limtt3t+2(2t1)(t2+t+1)Ch. 3.R - Prob. 9ECh. 3.R - Prob. 10ECh. 3.R - 7-12 Find the limit. limx(4x2+3x2x)Ch. 3.R - Prob. 12ECh. 3.R - 13-15 Sketch the graph of a function that...Ch. 3.R - Prob. 14ECh. 3.R - Prob. 15ECh. 3.R - The figure shows the graph of the derivative f of...Ch. 3.R - 17-28 Use the guidelines of Section 3.5 to sketch...Ch. 3.R - Prob. 18ECh. 3.R - 17-28 Use the guidelines of Section 3.5 to sketch...Ch. 3.R - 17-28 Use the guidelines of Section 3.5 to sketch...Ch. 3.R - 17-28 Use the guidelines of Section 3.5 to sketch...Ch. 3.R - Prob. 22ECh. 3.R - Prob. 23ECh. 3.R - Prob. 24ECh. 3.R - Prob. 25ECh. 3.R - Prob. 26ECh. 3.R - Prob. 27ECh. 3.R - Prob. 28ECh. 3.R - Prob. 29ECh. 3.R - Prob. 30ECh. 3.R - Prob. 31ECh. 3.R - Prob. 32ECh. 3.R - Show that the equation 3x+2cosx+5=0 has exactly...Ch. 3.R - Prob. 34ECh. 3.R - By applying the Mean Value Theorem to the function...Ch. 3.R - For what values of the constants a and b is 1, 3 a...Ch. 3.R - Prob. 37ECh. 3.R - Find two positive integers such that the sum of...Ch. 3.R - Show that the shortest distance from the point...Ch. 3.R - Prob. 40ECh. 3.R - Find the smallest possible area of an isosceles...Ch. 3.R - Prob. 42ECh. 3.R - Prob. 43ECh. 3.R - Prob. 44ECh. 3.R - Prob. 45ECh. 3.R - Prob. 46ECh. 3.R - A hockey team plays in an arena with a seating...Ch. 3.R - Prob. 48ECh. 3.R - Prob. 49ECh. 3.R - Prob. 50ECh. 3.R - Prob. 51ECh. 3.R - Prob. 52ECh. 3.R - Prob. 53ECh. 3.R - Prob. 54ECh. 3.R - 55-58 Find f. f(t)=2t3sint,f(0)=5Ch. 3.R - Prob. 56ECh. 3.R - Prob. 57ECh. 3.R - Prob. 58ECh. 3.R - Prob. 59ECh. 3.R - Prob. 60ECh. 3.R - Prob. 61ECh. 3.R - Prob. 62ECh. 3.R - Prob. 63ECh. 3.R - In an automobile race along a straight road, car A...Ch. 3.R - A rectangular beam will be cut from a cylindrical...Ch. 3.R - If a projectile is fired with an initial velocity...Ch. 3.R - Prob. 67ECh. 3.R - Prob. 68ECh. 3.P - Show that |sinxcosx|2 for all xCh. 3.P - Prob. 2PCh. 3.P - Show that the inflection points of the curve...Ch. 3.P - Find the point on the parabola y=1x2 at which the...Ch. 3.P - Prob. 5PCh. 3.P - Water is flowing at a constant rate into a...Ch. 3.P - Prob. 7PCh. 3.P - Prob. 8PCh. 3.P - Prob. 9PCh. 3.P - An isosceles triangle is circumscribed about the...Ch. 3.P - The line y=mx+b intersects the parabola y=x2 in...Ch. 3.P - Prob. 12PCh. 3.P - Prob. 13PCh. 3.P - Prob. 14PCh. 3.P - Prob. 15PCh. 3.P - a Let ABC be a triangle with right angle A and...Ch. 3.P - Prob. 17PCh. 3.P - ABCD is a square piece of paper with sides of...Ch. 3.P - Prob. 19PCh. 3.P - For what values of c is there is a straight line...Ch. 3.P - One of the problems posed by the Marquis de...Ch. 3.P - Prob. 22PCh. 3.P - Assume that a snowball melts so that its volume...Ch. 3.P - A hemispherical bubble is placed on a spherical...
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