Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 3, Problem 5RQ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
5. If f′(x) < 0 for 1 < x < 6, then f is decreasing on (1, 6).
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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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- Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardx4 -289 Consider the function f(x) = 2 X-17 Complete parts a and b below. a. Analyze lim f(x) and lim f(x), and then identify the horizontal asymptotes. x+x X--∞ lim 4 X-289 2 X∞ X-17 X - 289 lim = 2 ... X∞ X - 17 Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has a horizontal asymptote at y = B. The function has two horizontal asymptotes. The top asymptote is y = and the bottom asymptote is y = ☐ . C. The function has no horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. earrow_forwardExplain why lim x²-2x-35 X-7 X-7 lim (x+5), and then evaluate lim X-7 x² -2x-35 x-7 x-7 Choose the correct answer below. A. x²-2x-35 The limits lim X-7 X-7 and lim (x+5) equal the same number when evaluated using X-7 direct substitution. B. Since each limit approaches 7, it follows that the limits are equal. C. The numerator of the expression X-2x-35 X-7 simplifies to x + 5 for all x, so the limits are equal. D. Since x²-2x-35 X-7 = x + 5 whenever x 7, it follows that the two expressions evaluate to the same number as x approaches 7. Now evaluate the limit. x²-2x-35 lim X-7 X-7 = (Simplify your answer.)arrow_forwardA function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardEvaluate the following limit. lim X-X (10+19) Select the correct answer below and, if necessary, fill in the answer box within your choice. 10 A. lim 10+ = 2 ☐ (Type an integer or a simplified fraction.) X-∞ B. 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