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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (x + 4) x→1
Consider the graphs of the four functions g1, g2, g3, and g4.For each given condition of the function which of the graphs could be the graph of ƒ?a.b. ƒ is continuous at 2.c. 3 2 - 3 2 1 A + 2 -N 2 81 3 83 3 X 3 2 - 3 2 1 y + + 1 82 2 3 2 84 3 X X
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches 4 from the left and from the right. f(x) = -1 (x - 4)²
In Exercises find the limit L. Then use the ε-δ definition to prove that the limit is L. lim √√√x X x-9
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches -3 from the left and from the right by completing the table. Use a graphing utility to graph the function to confirm your answer. X f(x) X f(x) -3.5 -3.1 - 3.01 - 3.001 - 2.999 - 2.99 -2.9 -2.5 -3 ?
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches-3 from the left and from the right by completing the table.Use a graphing utility to graph the function to confirm youranswer. X f(x) X f(x) -3.5 -3.1 - 3.01 - 3.001 - 2.999 - 2.99 -2.9 -2.5 -3 ?
In Exercises find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (1-x²) x-2
In Exercises find the limit L. Then use the ε-δ definition to prove that the limit is L. lim 9 x-5
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches -3 from the left and from the right by completing the table. Use a graphing utility to graph the function to confirm your answer. X f(x) X f(x) -3.5 -3.1 - 3.01 - 3.001 - 2.999 - 2.99 -2.9 -2.5 -3 ?
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches -3 from the left and from the right by completing the table. Use a graphing utility to graph the function to confirm your answer. X f(x) X f(x) -3.5 -3.1 - 3.01 - 3.001 - 2.999 - 2.99 -2.9 -2.5 -3 ?
In Exercises find the vertical asymptotes (if any) of the graph of the function. f(x) = - 2 x²
Let be a nonzero constant. Prove that ifthenShow by means of an example that must be nonzero. lim f(x) = L, x-0
In Exercises find the vertical asymptotes (if any) of the graph of the function. f(x) 2 (x − 3)³
In Exercises find the vertical asymptotes (if any) of the graph of the function. t-zit ल (x)ƒ
In Exercises find the vertical asymptotes (if any) of the graph of the function. f(x) = 3x 2 x² + 9
In Exercises find the vertical asymptotes (if any) of the graph of the function. g(t) t - 1 +2 t² + 1
In Exercises find the vertical asymptotes (if any) of the graph of the function. h(s) = 3s + 4 2 S 16
In Exercises find the vertical asymptotes (if any) of the graph of the function. f(x) 3 7-x+zx
In Exercises find the vertical asymptotes (if any) of the graph of the function. 4x² + 4x - 24 2x39x2 18x + f(x) x4 - 2x³
In Exercises find the vertical asymptotes (if any) of the graph of the function. g(x) = +38 -3 x = 2
In Exercises find the vertical asymptotes (if any) of the graph of the function. h(x) = x² - 9 x³ + 3x² - x - 3 r3
In exercises find the limits.ƒ(x) = x + 7, g(x) = x²a.b.c. lim f(x) x-3
In Exercises find the vertical asymptotes (if any) of the graph of the function. h(t) t² - 2t -2 14 - 16
In Exercises find the vertical asymptotes (if any) of the graph of the function. f(x) = = x² - 2x - 15 x3 r3 – 5x2 + x − 5
In exercises find the limits.ƒ(x) = 5x, g(x) = x³a.b.c. lim f(x) x-1
In exercises find the limits.ƒ(x) = 4 − x², g(x) = √x + 1 a.b.c. lim f(x) x-1
In exercises find the limits.ƒ(x) = 2x² – 3x + 1, g(x) = 3√x + 6a.b.c. lim f(x) x-4
In Exercises find the vertical asymptotes (if any) of the graph of the function.ƒ(x) =CSC πX
In Exercises find the one-sided limit (if it exists). 1 lim x-1+ x + 1
In Exercises evaluate the limit given lim f(x) = − 6 and lim g(x) = 1. - x-c x-c
In Exercises determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = -1. Graph the function using a graphing utility to confirm your answer. f(x) = sin(x + 1) x + 1
In Exercises evaluate the limit given lim f(x) = − 6 and lim g(x) = 1. - x-c x-c
In Exercises find the vertical asymptotes (if any) of the graph of the function. (0)8 = tan 0 0
In Exercises find the vertical asymptotes (if any) of the graph of the function. s(t) = t sin t
In Exercises find the vertical asymptotes (if any) of the graph of the function.ƒ(x) = tan πX
In Exercises determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = -1. Graph the function using a graphing utility to confirm your answer. f(x) = x² - 1 2 x + 1
In Exercises evaluate the limit given lim f(x) = − 6 and lim g(x) = 1. - x-c x-c
In Exercises determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = -1. Graph the function using a graphing utility to confirm your answer. f(x) = = x² - 2x - 8 + 1 x
In Exercises evaluate the limit given lim f(x) = − 6 and lim g(x) = 1. - x-c x-c
In Exercises determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = -1. Graph the function using a graphing utility to confirm your answer. f(x) = = x² + 1 -2 x + 1
In Exercises find the one-sided limit (if it exists). lim x-1- -1 (x - 1)²
In Exercises find the one-sided limit (if it exists). X lim x 2 + x - 2
In Exercises find the one-sided limit (if it exists). x2 lim x2-x² + 4
In exercises use the information to evaluate the limits.a.b.c.d. lim f(x) = 3 x-c lim g(x) = 2 X-C
In Exercises use the position function s(t) = -4.9t² + 250, which gives the height (in meters) of an object that has fallen for t seconds from a height of 250 meters. The velocity at time t = a seconds is given byFind the velocity of the object when t = 4. lim t-a s(a) - s(t) a - t
In Exercises find the one-sided limit (if it exists). x + 3 lim x-3- x² + x - 6
In Exercises find the one-sided limit (if it exists). 6x² + x - 1 lim x→(-1/2) + 4x² - 4x - 3
In Exercises use the position function s(t) = -4.9t² + 250, which gives the height (in meters) of an object that has fallen for t seconds from a height of 250 meters. The velocity at time t = a seconds is given byAt what velocity will the object impact the ground? lim t-a s(a) - s(t) a - t
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) 1 4x²
In Exercises find the one-sided limit (if it exists). lim 1 + x→0- X
In Exercises find the one-sided limit (if it exists). lim | 6 x→0+ |- .13
In Exercises find the one-sided limit (if it exists). Tim (12 + 24)
In exercises use the information to evaluate the limits.a.b.c.d. lim f(x) = 4 X-C
In Exercises, find the limit (if it exists). If it does not exist, explain why. lim x-4- √√x - 2 x - 4 X
In Exercises find the one-sided limit (if it exists). X lim + cot x-3+3 TT.X 2
In Exercises, find the limit (if it exists). If it does not exist, explain why. lim x 3 |x - 3| x 3 -
In Exercises find the one-sided limit (if it exists). 2 lim x0+ sin x
In Exercises, find the limit (if it exists). If it does not exist, explain why. lim f(x), where f(x) = [(x − 2)², x ≤ 2 x-2 2 X, x > 2
In Exercises, find the limit (if it exists). If it does not exist, explain why. lim g(x), where g(x) x-1+ = [+++. x + 1, √1- x, x ≤ 1 x > 1
In Exercises find the one-sided limit (if it exists). lim x-(π/2) -2 COS X
In Exercises, find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x): = x + 3 x² 3x - 18 -
In Exercises use a graphing utility to graph the function and determine the one-sided limit. f(x) = sec lim f(x) x-4+ TTX 8
In Exercises, find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = X X3 X - EX
Determine the value c of such that the function is continuous on the entire real number line. f(x) = = x + 3, Lex cx + 6, x ≤ 2 x > 2
In your own words, describe the meaning of an infinite limit. Is ∞ a real number?
Determine the values of b and c such that the function is continuous on the entire real number line. f(x) = x + 1, 1 < x < 3 [x² + bx + c₂ |x − 2| ≥ 1 -
In your own words, describe what is meant by an asymptote of a graph.
In Exercises, describe the intervals on which the function is continuous. f(x) = = 4x²7x2 x + 2
Use the graph of the function ƒ(see figure) to sketch the graph of g (x) = 1/ƒ(x) on the interval [-2, 3]. To print an enlarged copy of the graph.ƒ f -2 -1 - 2 y 2 3 X
Write a rational function with vertical asymptotes at x = 6 and x = −2, and with a zero at x = 3.
Does the graph of every rational function have a vertical asymptote? Explain.
In Exercises describe the intervals on which the function is continuous.ƒ(x) = − 3x² + 7
According to the theory of relativity, the mass m of a particle depends on its velocity v. That is,where mo is the mass when the particle is at rest and c is the speed of light. Find the limit of the mass as v approaches c from the left. m mo √√1 1- (v²/c²)
In Exercises, describe the intervals on which the function is continuous. f(x) = √√√√x - 4 X
Use a graphing utility to complete the table for each function and graph each function to estimate the limit. What is the value of the limit when the power of in the denominator is greater than 3?a.b.c.d. X f(x) 1 0.5 0.2 0.1 0.01 0.001 0.0001
For a quantity of gas at a constant temperature, the pressure P is inversely proportional to the volume V. What is the limit of P as V approaches 0 from the right? Explain what this means in the context of the problem. Pressure P Volume V
In Exercises, describe the intervals on which the function is continuous. [ε + x]] = (x)ƒ
In Exercises, describe the intervals on which the function is continuous. f(x) = 5 - X, 2x3, x ≤ 2 x > 2
In Exercises, describe the intervals on which the function is continuous. f(x) = = 3x²-x-2 x - 1 0, x 1 x = 1
A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, then the top will move down the wall at a rate ofwhere x is the distance between the base of the ladder and the house, and r is the rate in feet per
On a trip of d miles to another city, a truck driver's average speed was x miles per hour. On the return trip, the average speed was y miles per hour. The average speed for the round trip was 50 miles per hour.(a) Verify thatWhat is the domain?(b) Complete the table.Are the values of y different
Consider the shaded region outside the sector of a circle of radius 10 meters and inside a right triangle (see figure).(a) Write the area A = ƒ(θ) of the region as a function of θ. Determine the domain of the function.(b) Use a graphing utility to complete the table and graph thefunction over
A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40-centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.(a) Determine the number of revolutions per minute of the saw.(b) How does crossing the
The cost of sending an overnight package from New York to Atlanta is $12.80 for the first pound and $2.50 for each additional pound or fraction thereof. Use the greatest integer function to create a model for the cost C of overnight delivery of a package weighing x pounds. Sketch the graph of this
In Exercises, find the vertical asymptotes (if any) of the graph of the function. f(x) = 3 X
LetFind each limit (if it exists).a.b.c. f(x) = = x² - 4 2 |x2|*
In Exercises, find the vertical asymptotes (if any) of the graph of the function. f(x) = 5 (x - 2)4
Use the graph of ƒ to identify the values of c for which exists.a.b. lim f(x) X-C
In Exercises, find the vertical asymptotes (if any) of the graph of the function. f(x): = x3 x² - 9 -2
Find functions ƒ and g such that lim f(x) = X-C and lim g(x) = = X-C ∞, but lim [f(x) − g(x)] ‡ 0. X→C
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The graphs of polynomial functions have no vertical asymptotes.
In Exercises, find the vertical asymptotes (if any) of the graph of the function. h (x) = 6.x 36 - x²
In Exercises, find the one-sided limit (if it exists). lim x-1- x² + 2x + 1 x = 1
In Exercises , find the vertical asymptotes (if any) of the graph of the function. g(x) = 2x + 1 x² - 64 -2
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The graphs of trigonometric functions have no vertical asymptotes.
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If ƒ has a vertical asymptote at x = 0, then ƒ is undefined atx = 0.
In Exercises, find the one-sided limit (if it exists). x+1 lim x→−1+ x3 + 1
Prove that ifThenDoes not exist. lim X-C 1 f(x) = 0
In Exercises use the – definition of infinite limits to prove the statement. 1 lim x3+ x - 3 = ∞
In Exercises, find the one-sided limit (if it exists). lim x-2- 1 3x² - 4
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