Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 1.6, Problem 19E
Evaluate the limit, if it exists.
19.
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Chapter 1 Solutions
Single Variable Calculus
Ch. 1.1 - If f(x)=x+2x and g(u)=u+2u, is it true that f = g?Ch. 1.1 - If f(x)=x2xx1andg(x)=x is it true that f = g?Ch. 1.1 - The graph of a function f is given. (a) State the...Ch. 1.1 - The graphs of f and g are given. (a) State the...Ch. 1.1 - Figure 1 was recorded by an instrument operated by...Ch. 1.1 - Prob. 6ECh. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Prob. 10E
Ch. 1.1 - Shown is a graph of the global average temperature...Ch. 1.1 - Trees grow faster and form wider rings in warm...Ch. 1.1 - You put some ice cubes in a glass, fill the glass...Ch. 1.1 - Three runners compete in a 100-meter race. The...Ch. 1.1 - The graph shows the power consumption for a day in...Ch. 1.1 - Sketch a rough graph of the number of hours of...Ch. 1.1 - Prob. 17ECh. 1.1 - Sketch a rough graph of the market value of a new...Ch. 1.1 - Sketch the graph of the amount of a particular...Ch. 1.1 - You place a frozen pie in an oven and bake it for...Ch. 1.1 - A homeowner mows the lawn every Wednesday...Ch. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a),...Ch. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Find the domain of the function. 35. h(x)=1x25x4Ch. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Find the domain and range and sketch the graph of...Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Sketch the graph of the function. 48. h(t) = |t| +...Ch. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Prob. 51ECh. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - A Norman window has the shape of a rectangle...Ch. 1.1 - A box with an open top is to be constructed from a...Ch. 1.1 - A cell phone plan has a basic charge of 35 a...Ch. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - In a certain country, income tax is assessed as...Ch. 1.1 - Prob. 68ECh. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - Prob. 71ECh. 1.1 - Prob. 72ECh. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Prob. 76ECh. 1.1 - Prob. 77ECh. 1.1 - Prob. 78ECh. 1.1 - If f and g are both even functions, is f + g even?...Ch. 1.1 - Prob. 80ECh. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Prob. 3ECh. 1.2 - Match each equation with its graph. Explain your...Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Find expressions for the quadratic functions whose...Ch. 1.2 - Find an expression for a cubic function f if f(1)...Ch. 1.2 - Prob. 12ECh. 1.2 - If the recommended adult dosage for a drug is D...Ch. 1.2 - The manager of a weekend flea market knows from...Ch. 1.2 - Prob. 15ECh. 1.2 - Jason leaves Detroit at 2:00 pm and drives at a...Ch. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - The monthly cost of driving a car depends on the...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.3 - Suppose the graph of f is given. Write equations...Ch. 1.3 - Explain how each graph is obtained from the graph...Ch. 1.3 - The graph of y = f(x) is given. Match each...Ch. 1.3 - The graph of f is given. Draw the graphs of the...Ch. 1.3 - The graph of f is given. Use it to graph the...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - A variable star is one whose brightness...Ch. 1.3 - Some of the highest tides in the world occur in...Ch. 1.3 - In a normal respiratory cycle the volume of air...Ch. 1.3 - Prob. 29ECh. 1.3 - Use the given graph of f to sketch the graph of y...Ch. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Find f g h. 42. f(x) = tan x, g(x)=xx1,h(x)=x3Ch. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - Express the function in the form f g. 47. v(t) =...Ch. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Express the function in the form f g h. 51. S(t)...Ch. 1.3 - Prob. 52ECh. 1.3 - Use the given graphs of f and g to evaluate each...Ch. 1.3 - Use the given graphs of f and g to estimate the...Ch. 1.3 - A stone is dropped into a lake, creating a...Ch. 1.3 - Prob. 56ECh. 1.3 - A ship is moving at a speed of 30 km/h parallel to...Ch. 1.3 - Prob. 58ECh. 1.3 - The Heaviside function H is defined by...Ch. 1.3 - The Heaviside function defined in Exercise 59 can...Ch. 1.3 - Let f and g be linear functions with equations...Ch. 1.3 - Prob. 62ECh. 1.3 - Prob. 63ECh. 1.3 - Prob. 64ECh. 1.3 - Prob. 65ECh. 1.3 - Suppose g is an odd function and let h = f g. Is...Ch. 1.4 - A tank holds 1000 gallons of water, which drains...Ch. 1.4 - A cardiac monitor is used to measure the heart...Ch. 1.4 - The point P(2, 1) lies on the curve y = 1/(1 x)....Ch. 1.4 - The point P(0.5, 0) lies on the curve y = cos x....Ch. 1.4 - If a ball is thrown into the air with a velocity...Ch. 1.4 - If a rock is thrown upward on the planet Mars with...Ch. 1.4 - The table shows the position of a motorcyclist...Ch. 1.4 - The displacement (in centimeters) of a particle...Ch. 1.4 - The point P(1, 0) lies on the curve y = sin(10/x)....Ch. 1.5 - Prob. 1ECh. 1.5 - Explain what it means to say that...Ch. 1.5 - Explain the meaning of each of the following. (a)...Ch. 1.5 - Use the given graph of f to state the value of...Ch. 1.5 - For the function f whose graph is given, state the...Ch. 1.5 - For the function h whose graph is given, state the...Ch. 1.5 - For the function g whose graph is given, state the...Ch. 1.5 - For the function A whose graph is shown, state the...Ch. 1.5 - For the function f whose graph is shown, state the...Ch. 1.5 - A patient receives a 150-mg injection of a drug...Ch. 1.5 - Sketch the graph of the function and use it to...Ch. 1.5 - Sketch the graph of the function and use it to...Ch. 1.5 - Use the graph of the function f to state the value...Ch. 1.5 - Use the graph of the function f to state the value...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Use a table of values to estimate the value of the...Ch. 1.5 - Use a table of values to estimate the value of the...Ch. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Determine the infinite limit. 29. limx5+x+1x5Ch. 1.5 - Determine the infinite limit. 30. limx5x+1x5Ch. 1.5 - Prob. 31ECh. 1.5 - Determine the infinite limit. 32. limx3x(x3)5Ch. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.5 - Determine the infinite limit. 37. limx2xcscxCh. 1.5 - Prob. 38ECh. 1.5 - Determine the infinite limit. 39....Ch. 1.5 - Prob. 40ECh. 1.5 - Determine limx11x31and limx1+1x31 (a) by...Ch. 1.5 - Prob. 42ECh. 1.5 - (a) Evaluate the function f(x) = x2 (2x/1000) for...Ch. 1.5 - (a) Evaluate h(x) = (tan x x)/x3 for x = 1, 0.5,...Ch. 1.5 - Graph the function f(x) = sin(/x) of Example 4 in...Ch. 1.5 - Consider the function f(x)=tan1x. (a) Show that...Ch. 1.5 - Prob. 47ECh. 1.5 - Prob. 48ECh. 1.5 - (a) Use numerical and graphical evidence to guess...Ch. 1.6 - Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find...Ch. 1.6 - The graphs of f and g are given. Use them to...Ch. 1.6 - Prob. 3ECh. 1.6 - Prob. 4ECh. 1.6 - Prob. 5ECh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Evaluate the limit and justify each step by...Ch. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Evaluate the limit, if it exists. 13....Ch. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Evaluate the limit, if it exists. 19. limx2x+2x3+8Ch. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Prob. 24ECh. 1.6 - Evaluate the limit, if it exists. 25. limt01+t1ttCh. 1.6 - Evaluate the limit, if it exists. 26....Ch. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 30ECh. 1.6 - Evaluate the limit, if it exists. 31....Ch. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Use the Squeeze Theorem to show that limx0 (x2 cos...Ch. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - If 2x g(x) x4 x2 + 2 for all x, evaluate...Ch. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - The signum (or sign) function, denoted by sgn, is...Ch. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.6 - Let B(t)={412tift2t+cift2 Find the value of c so...Ch. 1.6 - Let g(x)={xifx13ifx=12x2if1x2x3ifx2 (a) Evaluate...Ch. 1.6 - Prob. 53ECh. 1.6 - Let f(x) = cos x, x . (a) Sketch the graph of...Ch. 1.6 - If f(x) = x + x, show that limx2 f(x) exists but...Ch. 1.6 - Prob. 56ECh. 1.6 - If p is a polynomial, show that limxa p(x) = p(a).Ch. 1.6 - If r is a rational function, use Exercise 57 to...Ch. 1.6 - If limx1f(x)8x1=10, find limx1f(x).Ch. 1.6 - Prob. 60ECh. 1.6 - Prob. 61ECh. 1.6 - Prob. 62ECh. 1.6 - Show by means of an example that limxa [f(x) g(x)]...Ch. 1.6 - Prob. 64ECh. 1.6 - Is there a number a such that limx23x2+ax+a+3x2+x2...Ch. 1.6 - Prob. 66ECh. 1.7 - Use the given graph of f to find a number such...Ch. 1.7 - Prob. 2ECh. 1.7 - Use the given graph of f(x)=x to find a number ...Ch. 1.7 - Use the given graph of f(x) = x2 to find a number ...Ch. 1.7 - Prob. 5ECh. 1.7 - Prob. 6ECh. 1.7 - For the limit limx2(x33x+4)=6 illustrate...Ch. 1.7 - Prob. 8ECh. 1.7 - (a) Use a graph to find a number such that...Ch. 1.7 - Given that limxcsc2x=, illustrate Definition 6 by...Ch. 1.7 - Prob. 11ECh. 1.7 - A crystal growth furnace is used in research to...Ch. 1.7 - Prob. 13ECh. 1.7 - Given that limx2 (5x 7) = 3, illustrate...Ch. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prove the statement using the , definition of a...Ch. 1.7 - Prove the statement using the , definition of a...Ch. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Prob. 36ECh. 1.7 - Prove that limxax=a if a 0. [Hint:Usexa=xax+a.]Ch. 1.7 - Prob. 38ECh. 1.7 - Prob. 39ECh. 1.7 - Prob. 40ECh. 1.7 - Prob. 41ECh. 1.7 - Prob. 42ECh. 1.7 - Prob. 43ECh. 1.7 - Prob. 44ECh. 1.8 - Write an equation that expresses the fact that a...Ch. 1.8 - If f is continuous on (, ), what can you say about...Ch. 1.8 - (a) From the graph of f, state the numbers at...Ch. 1.8 - From the graph of g, state the intervals on which...Ch. 1.8 - Sketch the graph of a function f that is...Ch. 1.8 - Prob. 6ECh. 1.8 - Sketch the graph of a function f that is...Ch. 1.8 - Prob. 8ECh. 1.8 - The toll T charged for driving on a certain...Ch. 1.8 - Prob. 10ECh. 1.8 - Use the definition of continuity and the...Ch. 1.8 - Prob. 12ECh. 1.8 - Prob. 13ECh. 1.8 - Prob. 14ECh. 1.8 - Use the definition of continuity and the...Ch. 1.8 - Prob. 16ECh. 1.8 - Prob. 17ECh. 1.8 - Prob. 18ECh. 1.8 - Explain why the function is discontinuous at the...Ch. 1.8 - Prob. 20ECh. 1.8 - Explain why the function is discontinuous at the...Ch. 1.8 - Prob. 22ECh. 1.8 - Prob. 23ECh. 1.8 - How would you remove the discontinuity of f? In...Ch. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - Explain, using Theorems 4, 5, 7, and 9, why the...Ch. 1.8 - Prob. 28ECh. 1.8 - Prob. 29ECh. 1.8 - Prob. 30ECh. 1.8 - Prob. 31ECh. 1.8 - Prob. 32ECh. 1.8 - Locate the discontinuities of the function and...Ch. 1.8 - Prob. 34ECh. 1.8 - Prob. 35ECh. 1.8 - Prob. 36ECh. 1.8 - Prob. 37ECh. 1.8 - Prob. 38ECh. 1.8 - Prob. 39ECh. 1.8 - Prob. 40ECh. 1.8 - Prob. 41ECh. 1.8 - Find the numbers at which f is discontinuous. At...Ch. 1.8 - Find the numbers at which f is discontinuous. At...Ch. 1.8 - The gravitational force exerted by the planet...Ch. 1.8 - For what value of the constant c is the function f...Ch. 1.8 - Find the values of a and b that make f continuous...Ch. 1.8 - Suppose f and g are continuous functions such that...Ch. 1.8 - Prob. 48ECh. 1.8 - Which of the following functions f has a removable...Ch. 1.8 - Suppose that a function f is continuous on [0, 1]...Ch. 1.8 - If f(x) = x2 + 10 sin x, show that there is a...Ch. 1.8 - Suppose f is continuous on [1, 5] and the only...Ch. 1.8 - Prob. 53ECh. 1.8 - Use the Intermediate Value Theorem to show that...Ch. 1.8 - Prob. 55ECh. 1.8 - Prob. 56ECh. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - Prove, without graphing, that the graph of the...Ch. 1.8 - Prove, without graphing, that the graph of the...Ch. 1.8 - Prove that f is continuous at a if and only if...Ch. 1.8 - Prob. 64ECh. 1.8 - Prob. 65ECh. 1.8 - Prob. 66ECh. 1.8 - Prob. 67ECh. 1.8 - For what values of x is g continuous?...Ch. 1.8 - Prob. 69ECh. 1.8 - If a and b are positive numbers, prove that the...Ch. 1.8 - Prob. 71ECh. 1.8 - Prob. 72ECh. 1.8 - A Tibetan monk leaves the monastery at 7:00 am and...Ch. 1 - (a) What is a function? What are its domain and...Ch. 1 - Prob. 2RCCCh. 1 - Prob. 3RCCCh. 1 - Prob. 4RCCCh. 1 - Prob. 5RCCCh. 1 - Prob. 6RCCCh. 1 - Prob. 7RCCCh. 1 - Draw, by hand, a rough sketch of the graph of each...Ch. 1 - Prob. 9RCCCh. 1 - Prob. 10RCCCh. 1 - Prob. 11RCCCh. 1 - Prob. 12RCCCh. 1 - Prob. 13RCCCh. 1 - Prob. 14RCCCh. 1 - Prob. 15RCCCh. 1 - Prob. 16RCCCh. 1 - Prob. 17RCCCh. 1 - Prob. 18RCCCh. 1 - Prob. 19RCCCh. 1 - Prob. 1RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 3RQCh. 1 - Prob. 4RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 7RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 9RQCh. 1 - Prob. 10RQCh. 1 - Prob. 11RQCh. 1 - Prob. 12RQCh. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - Prob. 16RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 18RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 20RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 22RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 25RQCh. 1 - Prob. 26RQCh. 1 - Prob. 27RQCh. 1 - Let f be the function whose graph is given. (a)...Ch. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - The graph of f is given. Draw the graphs of the...Ch. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - A small-appliance manufacturer finds that it costs...Ch. 1 - The graph of f is given. (a) Find each limit, or...Ch. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Find the limit. 33. limu1u41u3+5u26uCh. 1 - Find the limit. 34. limx3x+6xx33x2Ch. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - If 2x 1 f(x) x2 for 0 x 3, find limx1 f(x).Ch. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Show that the function is continuous on its...Ch. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - Prob. 5PCh. 1 - Prob. 6PCh. 1 - The notation max{a, b, } means the largest of the...Ch. 1 - Prob. 8PCh. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prove that if n is a positive integer, then 7n 1...Ch. 1 - Prob. 12PCh. 1 - Prob. 13PCh. 1 - Prob. 14PCh. 1 - Prob. 15PCh. 1 - Find numbers a and b such that limx0ax+b2x=1.Ch. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Evaluate the following limits, if they exist,...Ch. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - A fixed point of a function f is a number c in its...Ch. 1 - Prob. 23PCh. 1 - (a) The figure shows an isosceles triangle ABC...Ch. 1 - Prob. 25P
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- The Cartesian coordinates of a point are given. (a) (4,-4) (i) Find polar coordinates (r, e) of the point, where r > 0 and 0 0 and 0 < 0 < 2π. (r, 6) = X 7 (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 0 < 2π. (r, 0) = Xarrow_forwardr>0 (r, 0) = T 0 and one with r 0 2 (c) (9,-17) 3 (r, 8) (r, 8) r> 0 r<0 (r, 0) = (r, 8) = X X X x x Warrow_forward74. Geometry of implicit differentiation Suppose x and y are related 0. Interpret the solution of this equa- by the equation F(x, y) = tion as the set of points (x, y) that lie on the intersection of the F(x, y) with the xy-plane (z = 0). surface Z = a. Make a sketch of a surface and its intersection with the xy-plane. Give a geometric interpretation of the result that dy dx = Fx F χ y b. Explain geometrically what happens at points where F = 0. yarrow_forward
- Example 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forwardConstruct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forward
- Use the graph to find the following limits. (a) lim f(x) (b) lim f(x) X-1 x→1 (a) Find lim f(x) or state that it does not exist. Select the correct choice X-1 below and, if necessary, fill in the answer box within your choice. OA. lim f(x) = X-1 (Round to the nearest integer as needed.) OB. The limit does not exist. Qarrow_forwardOfficials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forwardDecide from the graph whether each limit exists. If a limit exists, estimate its value. (a) lim F(x) X➡-7 (b) lim F(x) X-2 (a) What is the value of the limit? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. lim F(x) = X-7 (Round to the nearest integer as needed.) OB. The limit does not exist. 17 Garrow_forward
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