Single Variable Calculus
Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Chapter 3.7, Problem 47E

In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end as in the figure. It is believed that bees form their cells in such a way as to minimize the surface area for a given side length and height, thus using the least amount of wax in cell construction. Examination of these cells has shown that the measure of the apex angle θ is amazingly consistent. Based on the geometry of the cell, it can be shown that the surface area S is given by

S = 6 s h − 3 2 s 2 cot θ + ( 3 s 2 3 / 2 ) csc θ

where s, the length of the sides of the hexagon, and h, the height, are constants.

  1. (a) Calculate dS/dθ.
  2. (b) What angle should the bees prefer?
  3. (c) Determine the minimum surface area of the cell (in terms of s and h).

Note: Actual measurements of the angle θ in beehives have been made, and the measures of these angles seldom differ from the calculated value by more than 2°.

Chapter 3.7, Problem 47E, In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the

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Chapter 3 Solutions

Single Variable Calculus

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 - Prob. 8ECh. 3.1 - Sketch the graph of a function f that is...Ch. 3.1 - Prob. 10E
Ch. 3.1 - (a) Sketch the graph of a function that has a...Ch. 3.1 - Prob. 12ECh. 3.1 - (a) Sketch the graph of a function on [1, 2] that...Ch. 3.1 - (a) Sketch the graph of a function that has two...Ch. 3.1 - Prob. 15ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 3.1 - Prob. 26ECh. 3.1 - Sketch the graph of f by hand and use your sketch...Ch. 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 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Find the critical numbers of the function. 37....Ch. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Find the critical numbers of the function. 41. f()...Ch. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 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 - Find the absolute maximum and absolute minimum...Ch. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Find the absolute maximum and absolute minimum...Ch. 3.1 - If a and b are positive numbers, find the maximum...Ch. 3.1 - Use a graph to estimate the critical numbers of...Ch. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - (a) Use a graph to estimate the absolute maximum...Ch. 3.1 - Between 0C and 30C, the volume V (in cubic...Ch. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - On May 7, 1992, the space shuttle Endeavour was...Ch. 3.1 - When a foreign object lodged in the trachea...Ch. 3.1 - Show that 5 is a critical number of the function...Ch. 3.1 - Prove that the function f(x)=x101+x51+x+1 has...Ch. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 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]...Ch. 3.2 - The graph of a function g is shown. (a) Verify...Ch. 3.2 - Draw the graph of a function that is continuous on...Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Verify that the function satisfies the three...Ch. 3.2 - Prob. 8ECh. 3.2 - Let f(x) = 1 x2/3. Show that f(1) = f(1) but...Ch. 3.2 - Let f(x) = tan x. Show that f(0) = f() but there...Ch. 3.2 - Verify that the function satisfies the hypotheses...Ch. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Verify that the function satisfies the hypotheses...Ch. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Let f(x) = (x 3)2. Show that there is no value of...Ch. 3.2 - Let f(x) = 2 |2x 1|. Show that there is no value...Ch. 3.2 - Show that the equation has exactly one real root....Ch. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Show that the equation x4 + 4x + c = 0 has at most...Ch. 3.2 - (a) Show that a polynomial of degree 3 has at most...Ch. 3.2 - (a) Suppose that f is differentiable on and has...Ch. 3.2 - If f(1) = 10 and f(x) 2 for 1 x 4, how small...Ch. 3.2 - Suppose that 3 f(x) 5 for all values of x. Show...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Show that sin x x if 0 x 2.Ch. 3.2 - Prob. 30ECh. 3.2 - Use the Mean Value Theorem to prove the inequality...Ch. 3.2 - If f(x) = c (c a constant) for all x, use...Ch. 3.2 - Let f(x) = 1/x and g(x)={1xifx01+1xifx0 Show that...Ch. 3.2 - Prob. 34ECh. 3.2 - Two runners start a race at the same time and...Ch. 3.2 - Prob. 36ECh. 3.3 - Use the given graph of f to find the following....Ch. 3.3 - Use the given graph of f to find the following....Ch. 3.3 - Suppose you are given a formula for a function f....Ch. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - The graph of the derivative f of a function f is...Ch. 3.3 - In each part state the x-coordinates of the...Ch. 3.3 - Prob. 8ECh. 3.3 - (a) Find the intervals on which f is increasing or...Ch. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Find the local maximum and minimum values of f...Ch. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - (a) Find the critical numbers of f(x) = x4(x 1)3....Ch. 3.3 - Suppose f is continuous on (, ). (a) If f(2) = 0...Ch. 3.3 - Prob. 20ECh. 3.3 - Sketch the graph of a function that satisfies all...Ch. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Sketch the graph of a function that satisfies all...Ch. 3.3 - Sketch the graph of a function that satisfies all...Ch. 3.3 - Sketch the graph of a function that satisfies all...Ch. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - The graph of a function y = f(x) is shown. At...Ch. 3.3 - The graph of the derivative f of a continuous...Ch. 3.3 - The graph of the derivative f of a continuous...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - (a) Find the intervals of increase or decrease....Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - (a) Find the intervals of increase or decrease....Ch. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - (a) Find the intervals of increase or decrease....Ch. 3.3 - Suppose the derivative of a function f is f(x) =...Ch. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - (a) Use a graph of f to estimate the maximum and...Ch. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 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...Ch. 3.3 - For what values of a and b is (2, 2.5) an...Ch. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Show that tan x x for 0 x /2, [Hint: Show that...Ch. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - For what values of c does the polynomial P(x) = x4...Ch. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Show that the function g(x) = x |x| has an...Ch. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Prob. 77ECh. 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 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - (a) Estimate the value of limx(x2+x+1+x)by...Ch. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Find the horizontal and vertical asymptotes of...Ch. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - (a) Graph the function f(x)=2x2+13x5How many...Ch. 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 f that satisfies the...Ch. 3.4 - Prob. 46ECh. 3.4 - A function f is a ratio of quadratic functions and...Ch. 3.4 - Find the horizontal asymptotes of the curve and...Ch. 3.4 - Find the horizontal asymptotes of the curve and...Ch. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Find the limits as x and as x . Use this...Ch. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Sketch the graph of a function that satisfies all...Ch. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - Prob. 61ECh. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - (a) How large do we have to take x so that...Ch. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 2ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 4ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Use the guidelines of this section to sketch the...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 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 37ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - In the theory of relativity, the mass of a...Ch. 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 - Prob. 45ECh. 3.5 - Find an equation of the slant asymptote. Do not...Ch. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Use the guidelines of this section to sketch the...Ch. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Show that the curve y=x2+4x has two slant...Ch. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.6 - Produce graphs of f that reveal all the important...Ch. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Produce graphs of f that reveal all the important...Ch. 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 - Sketch the graph by hand using asymptotes and...Ch. 3.6 - Prob. 12ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Describe how the graph of f varies as c varies....Ch. 3.6 - Describe how the graph of f varies as c varies....Ch. 3.6 - Prob. 25ECh. 3.6 - Investigate the family of curves given by the...Ch. 3.6 - Prob. 27ECh. 3.6 - (a) Investigate the family of polynomials given by...Ch. 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 - Prob. 4ECh. 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 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - The rate (in mg carbon/m3/h) at which...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 - A box with a square base and open top must have a...Ch. 3.7 - Prob. 15ECh. 3.7 - A rectangular storage container with an open top...Ch. 3.7 - Prob. 17ECh. 3.7 - A farmer wants to fence in a rectangular plot of...Ch. 3.7 - If the farmer in Exercise 18 wants to enclose 8000...Ch. 3.7 - Prob. 20ECh. 3.7 - Prob. 21ECh. 3.7 - Find the point on the curve y=x that is closest to...Ch. 3.7 - Find the points on the ellipse 4x2 + y2 = 4 that...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 - Prob. 27ECh. 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 - Prob. 30ECh. 3.7 - Prob. 31ECh. 3.7 - Prob. 32ECh. 3.7 - Prob. 33ECh. 3.7 - A Norman window has the shape of a rectangle...Ch. 3.7 - Prob. 35ECh. 3.7 - Prob. 36ECh. 3.7 - Prob. 37ECh. 3.7 - Solve Exercise 37 if one piece is bent into a...Ch. 3.7 - Prob. 39ECh. 3.7 - Prob. 40ECh. 3.7 - A cone-shaped drinking cup is made from a circular...Ch. 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 - If a resistor of R ohms is connected across a...Ch. 3.7 - Prob. 46ECh. 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 - Prob. 51ECh. 3.7 - Prob. 52ECh. 3.7 - Prob. 53ECh. 3.7 - Prob. 54ECh. 3.7 - Let a and b be positive numbers. Find the length...Ch. 3.7 - At which points on the curve y = 1 + 40x3 3x5...Ch. 3.7 - What is the shortest possible length of the line...Ch. 3.7 - Prob. 58ECh. 3.7 - Prob. 59ECh. 3.7 - (a) Show that if the profit P(x) is a maximum,...Ch. 3.7 - A baseball team plays in a stadium that holds...Ch. 3.7 - Prob. 62ECh. 3.7 - Prob. 63ECh. 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 - Find the maximum area of a rectangle that can be...Ch. 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,...Ch. 3.8 - Use Newtons method with the specified initial...Ch. 3.8 - Prob. 7ECh. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Use Newtons method to approximate the given number...Ch. 3.8 - Use Newtons method to approximate the given number...Ch. 3.8 - (a) Explain how we know that the given equation...Ch. 3.8 - Prob. 14ECh. 3.8 - Use Newtons method to approximate the indicated...Ch. 3.8 - Prob. 16ECh. 3.8 - Use Newtons method to find all solutions of the...Ch. 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 - (a) Apply Newtons method to the equation x2 a = 0...Ch. 3.8 - Prob. 28ECh. 3.8 - Explain why Newtons method doesnt work for finding...Ch. 3.8 - Prob. 30ECh. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - (a) Use Newtons method to find the critical...Ch. 3.8 - Use Newtons method to find the absolute maximum...Ch. 3.8 - Prob. 35ECh. 3.8 - Of the infinitely many lines that are tangent to...Ch. 3.8 - Prob. 37ECh. 3.8 - In the figure, the length of the chord AB is 4 cm...Ch. 3.8 - A car dealer sells a new car for 18,000. He also...Ch. 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 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 8ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 10ECh. 3.9 - Find the most general antiderivative of the...Ch. 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 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 18ECh. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Prob. 20ECh. 3.9 - Prob. 21ECh. 3.9 - Prob. 22ECh. 3.9 - Find f. 23. f(x) = 20x3 12x2 + 6xCh. 3.9 - Prob. 24ECh. 3.9 - f(x)=4x3Ch. 3.9 - Prob. 26ECh. 3.9 - Find f. 27. f(t) = 12 + sin tCh. 3.9 - Find f. 28. f(t)=t2costCh. 3.9 - Find f. 29. f(x)=1+3x,f(4)=25Ch. 3.9 - Prob. 30ECh. 3.9 - Prob. 31ECh. 3.9 - Prob. 32ECh. 3.9 - Find f. 33. f(t) = sec t (sec t + tan t), /2 t ...Ch. 3.9 - Prob. 34ECh. 3.9 - Find f. 35. f(x) = 2 + 12x 12x2, f(0) = 4, f(0) =...Ch. 3.9 - Prob. 36ECh. 3.9 - Prob. 37ECh. 3.9 - Prob. 38ECh. 3.9 - Prob. 39ECh. 3.9 - Prob. 40ECh. 3.9 - Find f. 41. f(t)=t3cost,f(0)=2,f(1)=2Ch. 3.9 - Prob. 42ECh. 3.9 - Given that the graph of f passes through the point...Ch. 3.9 - Find a function f such that f(x) = x3 and the line...Ch. 3.9 - The graph of a function f is shown. Which graph is...Ch. 3.9 - The graph of a function f is shown. Which graph is...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 - The graph of f is shown in the figure. Sketch the...Ch. 3.9 - Prob. 50ECh. 3.9 - Prob. 51ECh. 3.9 - Prob. 52ECh. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A stone is dropped from the upper observation deck...Ch. 3.9 - Prob. 60ECh. 3.9 - An object is projected upward with initial...Ch. 3.9 - Two balls are thrown upward from the edge of the...Ch. 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 - What constant acceleration is required to increase...Ch. 3.9 - Prob. 70ECh. 3.9 - A car is traveling at 100 km/h when the driver...Ch. 3.9 - A model rocket is fired vertically upward from...Ch. 3.9 - Prob. 73ECh. 3 - Explain the difference between an absolute maximum...Ch. 3 - What does the Extreme Value Theorem say?Ch. 3 - Prob. 3RCCCh. 3 - Prob. 4RCCCh. 3 - (a) State Rolles Theorem. (b) State the Mean Value...Ch. 3 - Prob. 6RCCCh. 3 - Prob. 7RCCCh. 3 - Prob. 8RCCCh. 3 - If you have a graphing calculator or computer, why...Ch. 3 - Prob. 10RCCCh. 3 - Prob. 11RCCCh. 3 - Prob. 1RQCh. 3 - Prob. 2RQCh. 3 - Prob. 3RQCh. 3 - Prob. 4RQCh. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 6RQCh. 3 - Prob. 7RQCh. 3 - Prob. 8RQCh. 3 - Prob. 9RQCh. 3 - Prob. 10RQCh. 3 - Prob. 11RQCh. 3 - Prob. 12RQCh. 3 - Prob. 13RQCh. 3 - Prob. 14RQCh. 3 - Prob. 15RQCh. 3 - Prob. 16RQCh. 3 - Prob. 17RQCh. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 19RQCh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Find the local and absolute extreme values of the...Ch. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Sketch the graph of a function that satisfies the...Ch. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - The figure shows the graph of the derivative f of...Ch. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - For what values of the constants a and b is (1, 3)...Ch. 3 - Let g(x) = f(x2), where f is twice differentiable...Ch. 3 - Prob. 38RECh. 3 - Show that the shortest distance from the point...Ch. 3 - Find the point on the hyperbola xy = 8 that is...Ch. 3 - Find the smallest possible area of an isosceles...Ch. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - A metal storage tank with volume V is to be...Ch. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Find f. 56. f(u)=u2+uu,f(1)=3Ch. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - A canister is dropped from a helicopter 500 m...Ch. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Show that the inflection points of the curve y =...Ch. 3 - Find the point on the parabola y = 1 x2 at which...Ch. 3 - Find the highest and lowest points on the curve x2...Ch. 3 - Water is flowing at a constant rate into a...Ch. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - An isosceles triangle is circumscribed about the...Ch. 3 - The line y = mx + b intersects the parabola y = x2...Ch. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Let ABC be a triangle with BAC = 120 and |AB| ...Ch. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - For what values of c is there a straight line that...Ch. 3 - One of the problems posed by the Marquis de...Ch. 3 - Assume that a snowball melts so that its volume...Ch. 3 - A hemispherical bubble is placed on a spherical...
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