Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 4.5, Problem 1E
Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum.
(a) Make a table of values, like the one at the right, so that the sum of the numbers in the first two columns is always 23. On the basis of the evidence in your table, estimate the answer to the problem.
(b) Use calculus to solve the problem and compare with your answer to part (a).
First number | Second number | Product |
1 | 22 | 22 |
2 | 21 | 42 |
3 | 20 | 60 |
⋮ | ⋮ | ⋮ |
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JANUARY 17, 2025
WORKSHEET 1
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1. Let f(x) = 2x-
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(d) Specify the domain and range of the function f.
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Chapter 4 Solutions
Essential Calculus: Early Transcendentals
Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Suppose f is a continuous function defined on a...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...
Ch. 4.1 - (a) Sketch the graph of a function that has a...Ch. 4.1 - (a) Sketch the graph of a function on [1, 2] that...Ch. 4.1 - (a) Sketch the graph of a function on [1, 2] that...Ch. 4.1 - (a) Sketch the graph of a function that has two...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Find the critical numbers of the function....Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the critical numbers of the function. g(t) =...Ch. 4.1 - Find the critical numbers of the function. g(t) =...Ch. 4.1 - Find the critical numbers of the function....Ch. 4.1 - Find the critical numbers of the function....Ch. 4.1 - Find the critical numbers of the function. F(x) =...Ch. 4.1 - Find the critical numbers of the function. g() = 4...Ch. 4.1 - Find the critical numbers of the function. f() = 2...Ch. 4.1 - Find the critical numbers of the function. g(x) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - If a and b are positive numbers, find the maximum...Ch. 4.1 - Use a graph to estimate the critical numbers of...Ch. 4.1 - (a) Use a graph to estimate the absolute maximum...Ch. 4.1 - (a) Use a graph to estimate the absolute maximum...Ch. 4.1 - (a) Use a graph to estimate the absolute maximum...Ch. 4.1 - (a) Use a graph to estimate the absolute maximum...Ch. 4.1 - Between 0C and 30C, the volume V (in cubic...Ch. 4.1 - An object with weight W is dragged along a...Ch. 4.1 - A model for the U S average price of a pound of...Ch. 4.1 - The Hubble Space Telescope was deployed April 24,...Ch. 4.1 - When a foreign object lodged in the trachea...Ch. 4.1 - Show that 5 is a critical number of the function...Ch. 4.1 - Prove that the function f(x)=x101+x51+x+1 has...Ch. 4.1 - If f has a local minimum value at c, show that the...Ch. 4.1 - Prove Fermats Theorem for the case in which f has...Ch. 4.1 - A cubic function is a polynomial of degree 3; that...Ch. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Let f(x) = 1 x2/3. Show that f(l) = f(1) but...Ch. 4.2 - Let f(x) = tan x. Show that f(0) = f() but there...Ch. 4.2 - Use the graph of f to estimate the values of c...Ch. 4.2 - Use the graph of f given in Exercise 7 to estimate...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Find the number c that satisfies the conclusion of...Ch. 4.2 - Find the number c that satisfies the conclusion of...Ch. 4.2 - Let f(x) = (x 3)2. Show that there is no value of...Ch. 4.2 - Let f(x) = 2 |2x 1|. Show that there is no value...Ch. 4.2 - Show that the equation has exactly one real root....Ch. 4.2 - Show that the equation has exactly one real root....Ch. 4.2 - Show that the equation x3 15x + c = 0 has at most...Ch. 4.2 - Show that the equation x4 + 4x + c = 0 has at most...Ch. 4.2 - (a) Show that a polynomial of degree 3 has at most...Ch. 4.2 - (a) Suppose that f is differentiable on and has...Ch. 4.2 - If f(1) = 10 and f(x) 2 for 1 x 4, how small...Ch. 4.2 - Suppose that 3 f(x) 5 for all values of x. Show...Ch. 4.2 - Does there exist a function f such that f(0) = 1,...Ch. 4.2 - Suppose that f and g are continuous on [a, b] and...Ch. 4.2 - Show that 1+x1+12xifx0.Ch. 4.2 - Suppose f is an odd function and is differentiable...Ch. 4.2 - Use the Mean Value Theorem to prove the inequality...Ch. 4.2 - If f(x) = c (c a constant) for all x, use...Ch. 4.2 - Let f(x) = l/x and g(x)={1xifx01+1xifx0 Show that...Ch. 4.2 - Use Theorem 5 to prove the identity...Ch. 4.2 - Prove the identity arcsinx1x+1=2arctanx2Ch. 4.2 - At 2:00 PM a cars speedometer reads 30 mi/h. At...Ch. 4.2 - Two runners start a race at the same time and...Ch. 4.2 - A number a is called a fixed point of a function f...Ch. 4.3 - In each part state the x-coordinates of the...Ch. 4.3 - The graph of the first derivative f of a function...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - Find the local maximum and minimum values of f...Ch. 4.3 - Find the local maximum and minimum values of f...Ch. 4.3 - (a) Find the critical numbers of f(x) = x4(x 1)3....Ch. 4.3 - Suppose f is continuous on (, ). (a) If f(2) = 0...Ch. 4.3 - 1720 Sketch the graph of a function that satisfies...Ch. 4.3 - Sketch the graph of a function that satisfies all...Ch. 4.3 - Sketch the graph of a function that satisfies all...Ch. 4.3 - Sketch the graph of a function that satisfies all...Ch. 4.3 - Sketch the graph of a function that satisfes all...Ch. 4.3 - Sketch the graph of a function that satisfes all...Ch. 4.3 - The graph of the derivative f of a continuous...Ch. 4.3 - The graph of the derivative f of a continuous...Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - Suppose the derivative of a function f is f(x) =...Ch. 4.3 - Use the methods of this section to sketch the...Ch. 4.3 - (a) Use a graph of f to estimate the maximum and...Ch. 4.3 - (a) Use a graph of f to estimate the maximum and...Ch. 4.3 - A drug response curve describes the level of...Ch. 4.3 - Prob. 50ECh. 4.3 - Find a cubic function f(x) = ax3 + bx2 + cx + d...Ch. 4.3 - For what values of the numbers a and b does the...Ch. 4.3 - (a) If the function f(x) = x3 + ax2 + bx has the...Ch. 4.3 - Show that the curve y = (1 + x)/(1 + x2) has three...Ch. 4.3 - Show that the curves y = ex and y = ex touch the...Ch. 4.3 - Show that the inflection points of the curve y = x...Ch. 4.3 - Show that tan x x for 0 x /2. [Hint: Show that...Ch. 4.3 - (a) Show that ex 1 + x for x 0. (b) Deduce that...Ch. 4.3 - Show that a cubic function (a third-degree...Ch. 4.3 - For what values of c does the polynomial P(x) = x4...Ch. 4.3 - Prove that if (c, f(c)) is a point of inflection...Ch. 4.3 - Show that if f(x) = x4, then f(0) = 0, but (0, 0)...Ch. 4.3 - Show that the function g(x) = x | x | has an...Ch. 4.3 - Suppose that f is continuous and f(c) = f(c) = 0,...Ch. 4.3 - Suppose f is differentiable on an interval I and...Ch. 4.3 - For what values of c is the function f(x)=cx+1x2+3...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - The table gives the population of the world P(t),...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Prob. 27ECh. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - 144 Use the guidelines of this section to sketch...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - In the theory of relativity, the mass of a...Ch. 4.4 - In the theory of relativity, the energy of a...Ch. 4.4 - The figure shows a beam of length L embedded in...Ch. 4.4 - Coulombs Law states that the force of attraction...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Use the guidelines of this section to sketch the...Ch. 4.4 - Show that the curve y = x tan1 x has two slant...Ch. 4.4 - Show that the curve y=x2+4x has two slant...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Produce graphs of f that reveal all the important...Ch. 4.4 - Describe how the graph of f varies as c varies....Ch. 4.4 - Describe how the graph of f varies as c varics....Ch. 4.4 - Describe how the graph of f varies as c varics....Ch. 4.4 - Describe how the graph of f varies as c varics....Ch. 4.4 - Describe how the graph of f varies as c varies....Ch. 4.4 - Investigate the family of curves given by the...Ch. 4.5 - Consider the following problem: Find two numbers...Ch. 4.5 - Find two numbers whose difference is 100 and whose...Ch. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Consider the following problem: A box with an open...Ch. 4.5 - Prob. 12ECh. 4.5 - Prob. 11ECh. 4.5 - A rectangular storage container with an open top...Ch. 4.5 - Prob. 13ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 55ECh. 4.6 - The figure shows the graph of a function f....Ch. 4.6 - Follow the instructions for Exercise 1 (a) but use...Ch. 4.6 - Prob. 3ECh. 4.6 - For each initial approximation, determine...Ch. 4.6 - Prob. 5ECh. 4.6 - Use Newtons method with the specified initial...Ch. 4.6 - Prob. 7ECh. 4.6 - Prob. 8ECh. 4.6 - Prob. 9ECh. 4.6 - Prob. 10ECh. 4.6 - Use Newtons method to approximate the given number...Ch. 4.6 - Prob. 12ECh. 4.6 - Prob. 13ECh. 4.6 - Prob. 14ECh. 4.6 - Prob. 15ECh. 4.6 - Prob. 16ECh. 4.6 - Prob. 17ECh. 4.6 - Prob. 18ECh. 4.6 - Prob. 21ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - Prob. 24ECh. 4.6 - Prob. 25ECh. 4.6 - Prob. 26ECh. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - Prob. 30ECh. 4.6 - Prob. 31ECh. 4.6 - Prob. 32ECh. 4.7 - Find the most general antiderivative of the...Ch. 4.7 - Find the most general antiderivative of the...Ch. 4.7 - Prob. 3ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Find the most general antiderivative of the...Ch. 4.7 - Prob. 9ECh. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Find f. f(x) = x6 4x4 + x + 1Ch. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Find f. f() = sin + cos , f(0) = 3, f(0) = 4Ch. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - A particle is moving with the given data. Find the...Ch. 4.7 - Prob. 43ECh. 4.7 - Prob. 44ECh. 4.7 - Prob. 45ECh. 4.7 - Prob. 46ECh. 4.7 - Prob. 47ECh. 4.7 - Prob. 48ECh. 4.7 - Prob. 49ECh. 4.7 - Prob. 50ECh. 4.7 - Prob. 51ECh. 4.7 - Prob. 52ECh. 4.7 - Prob. 53ECh. 4.7 - Prob. 54ECh. 4.7 - Prob. 55ECh. 4 - Prob. 44RECh. 4 - Prob. 1RCCCh. 4 - Prob. 2RCCCh. 4 - Prob. 3RCCCh. 4 - Prob. 4RCCCh. 4 - Prob. 5RCCCh. 4 - Prob. 6RCCCh. 4 - Prob. 7RCCCh. 4 - Prob. 8RCCCh. 4 - Prob. 9RCCCh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQCh. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 - Prob. 14RQCh. 4 - Prob. 15RQCh. 4 - Prob. 16RQCh. 4 - Prob. 17RQCh. 4 - Prob. 18RQCh. 4 - Prob. 19RQCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - The figure shows the graph of the derivative f of...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - 1524 Use the guidelines of Section 4.4 to sketch...Ch. 4 - Prob. 16RECh. 4 - Prob. 18RECh. 4 - Prob. 17RECh. 4 - Prob. 20RECh. 4 - Prob. 19RECh. 4 - Prob. 22RECh. 4 - Prob. 21RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 45RECh. 4 - A metal storage tank with volume V is to be...Ch. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 60RECh. 4 - Prob. 59RECh. 4 - Prob. 61RE
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- A cable television company estimates that with x thousand subscribers, its monthly revenue and cost (in thousands of dollars) are given by the following equations. R(x) = 45x - 0.24x2 C(x) = 257 + 13xarrow_forwardx³-343 If k(x) = x-7 complete the table and use the results to find lim k(x). X-7 x 6.9 6.99 6.999 7.001 7.01 7.1 k(x) Complete the table. X 6.9 6.99 6.999 7.001 7.01 7.1 k(x) (Round to three decimal places as needed.)arrow_forward(3) (4 points) Given three vectors a, b, and c, suppose: |bx c = 2 |a|=√√8 • The angle between a and b xc is 0 = 135º. . Calculate the volume a (bxc) of the parallelepiped spanned by the three vectors.arrow_forward
- Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g)…arrow_forwardThink of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector a--b geometrically?arrow_forward(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1). (a) (4 points) Using the dot product determine the angle between a and b. (b) (2 points) Determine the cross product vector axb. (c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify your answer. 1arrow_forward
- (d) (4 points) Think of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector ab geometrically? d be .dx adjarrow_forward(2) (4 points) Find all vectors v having length 1 that are perpendicular to both =(2,0,2) and j = (0,1,0). Show all work. a=arrow_forwardFor the following function, find the full power series centered at a of convergence. 0 and then give the first 5 nonzero terms of the power series and the open interval = f(2) Σ 8 1(x)--(-1)*(3)* n=0 ₤(x) = + + + ++... The open interval of convergence is: 1 1 3 f(x)= = 28 3x6 +1 (Give your answer in help (intervals) .)arrow_forward
- For the following function, find the full power series centered at x = 0 and then give the first 5 nonzero terms of the power series and the open interval of convergence. f(x) = Σ| n=0 9 f(x) = 6 + 4x f(x)− + + + ++··· The open interval of convergence is: ☐ (Give your answer in help (intervals) .)arrow_forwardLet X be a random variable with the standard normal distribution, i.e.,X has the probability density functionfX(x) = 1/√2π e^-(x^2/2)2 .Consider the random variablesXn = 20(3 + X6) ^1/2n e ^x^2/n+19 , x ∈ R, n ∈ N.Using the dominated convergence theorem, prove that the limit exists and find it limn→∞E(Xn)arrow_forwardLet X be a discrete random variable taking values in {0, 1, 2, . . . }with the probability generating function G(s) = E(sX). Prove thatVar(X) = G′′(1) + G′(1) − [G′(1)]2.[5 Marks](ii) Let X be a random variable taking values in [0,∞) with proba-bility density functionfX(u) = (5/4(1 − u^4, 0 ≤ u ≤ 1,0, otherwise. Let y =x^1/2 find the probability density function of Yarrow_forward
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