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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = [x, x ≤ 1 x², x > 1
In Exercise use a graphing utility to graph the function and estimate the limit (if it exists). What is the domain of the function? Can you detect a possible error in determining the domain of a
In Exercise use a graphing utility to graph the function and estimate the limit (if it exists). What is the domain of the function? Can you detect a possible error in determining the domain of a
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = √√√x + 1, x ≤ 2 2x 3 - x, x > 2
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = -2x + 3, x < 1 x², x ≥ 1
In Exercise use a graphing utility to graph the function and estimate the limit (if it exists). What is the domain of the function? Can you detect a possible error in determining the domain of a
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = TT X 4 177, [x] < 1 |x ≥ 1 tan (x₂
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = [-2.x, x ≤ 2 x² - 4x + 1, x > 2
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = CSC 2, TT X 6 |x - 3| ≤ 2 |x - 3|>2
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = tan TTX 2
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = [[x − 8]
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable?ƒ(x) = csc 2x
In Exercises find the limit (if it exists). If it does not exist, explain why. lim x--3- X x² - 9
In Exercises find the limit (if it exists). If it does not exist, explain why. lim 피 X-r
In Exercises find the limit (if it exists). If it does not exist, explain why. lim x 4 √x-2 x 4 -
In Exercises find the limit (if it exists). If it does not exist, explain why. lim x 10 |x - 10] x 10 -
In Exercises find the limit (if it exists). If it does not exist, explain why. lim Ar→0+ (x + 4x)2 + x + Δx – (x2 + x) - Δ.χ
In Exercises find the limit (if it exists). If it does not exist, explain why. lim Δr-0 1 x + 4x Δε 1 X
In Exercises find the limit (if it exists). If it does not exist, explain why. lim f(x), where f(x) = x-3 x < 3 √x² - 4x + 6, 1-x² + 4x2, x ≥ 3
In Exercises find the limit (if it exists). If it does not exist, explain why. lim f(x), where f(x) x-3- x + 2 2 12 - 2x 3 x ≤ 3 x > 3
In Exercises find the limit (if it exists). If it does not exist, explain why. lim f(x), where f(x) = = x-1 [x³ + 1, x < 1 x + 1, x ≥ 1
In Exercises find the limit (if it exists). If it does not exist, explain why. lim f(x), where f(x) x-1+ = X, 1 - X, x ≤ 1 x >1
In Exercises find the limit (if it exists). If it does not exist, explain why. lim sec x X→π/2
In Exercises find the limit (if it exists). If it does not exist, explain why. lim cot x X-T
In Exercises find the limit (if it exists). If it does not exist, explain why. lim (5[[x] - 7) x→4
In Exercises find the limit (if it exists). If it does not exist, explain why. lim (2x - [x]) x-2+
In Exercises find the limit (if it exists). If it does not exist, explain why. lim (2-[-x]) x→3
In Exercises find the limit (if it exists). If it does not exist, explain why. lim 1 x→1 X
In Exercises discuss the continuity of each function. f(x) -3 1 x² - 4 y 3 2 -1 -2 -3+ 3 X
In Exercises find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable? f(x) = 5 - [[x]
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. f(x) = 3x³, x ≤ 1 Lax ax + 5, x > 1
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. f(x) = = [3.x², ax - x ≥ 1 4. x < 1
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. f(x) = ax², x ≤ 2 x > 2
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. g(x) = = 4 sin x X x < 0 a 2x. x ≥ 0 -
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. 2, f(x) = ax + b₂ (-2, x ≤ 1 -1 < x < 3 x ≥3
In Exercises find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. g(x) = = x2 x² - a² x - a (8, x = a x = a
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)). S + zx = (x)8 で (x)ƒ 9-x I
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)).ƒ(x) = x2g(x) = x -1
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)). I - x = (x)8 x^ 1 f(x) =
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)).ƒ(x) = 5x + 1g(x) = x³
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)). f(x) = tan x g(x) || X 2
In Exercise consider the function ƒ(x) = √x.Is a true statement? Explain. lim√√√x = 0 x-0
In Exercises use a graphing utility to graph the function. Use the graph to determine any x-values at which the function is not continuous. x = [[x]]= (x) f
In Exercises use a graphing utility to graph the function. Use the graph to determine any x-values at which the function is not continuous. g(x) = [x² – 3x, 2x 5₁ x > 4 x ≤ 4
In Exercises use a graphing utility to graph the function. Use the graph to determine any x-values at which the function is not continuous. h(x) = 1 x² + 2x 15 -
In Exercises, discuss the continuity of the composite function ℏ(x) = ƒ(g(x)).ƒ(x) = sin xg(x) = x²
In Exercises use the position function s(t) = -4.9t² + 200, which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a
When using a graphing utility to generate a table to approximatea student concluded that the limit was 0.01745 rather than 1. Determine the probable cause of the error. sin x lim x-0 X
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. |x| lim = 1 x 0 X
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. sin x lim X-T X = 1
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 f(x) = g(x) for all real numbers other than x = 0, and lim
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 lim f(x) X-C = L, then f(c) = L.
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. lim f(x) = 3, where f(x) x-2 = 3, 0, x≤2 x > 2
In Exercises use the position function s(t) = -4.9t² + 200, which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a
Find two functions ƒ and g such thatdo not exist, butdoes exist. lim f(x) and lim g(x) x-0 x->0
Would you use the dividing out technique or the rationalizing technique to find the limit of the function? Explain your reasoning.a.b. lim 41-2 x² + x - 2 x + 2 2 1 + -3-2-1 -4+ 1 23 X
Prove thatis equivalent to lim f(x) = L X-C
(a) Find(b) Use your answer to part (a) to derive the approximation cos x ≈ 1 -1/2x² for x near 0.(c) Use your answer to part (b) to approximate cos(0.1).(d) Use a calculator to approximate
In Exercises use a graphing utility to graph the function. Use the graph to determine any x-values at which the function is not continuous. f(x) = cos x - 1 5x, X x < 0 x ≥ 0
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 f(x) < g(x) for all x ‡ a, then lim f(x) < lim g(x). x-a x-a
Consider (a) Find the domain of ƒ.(b) Use a graphing utility to graph ƒ. Is the domain of ƒ obvious from the graph? If not, explain.(c) Use the graph of ƒ to approximate(d) Confirm your
In exercises use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. x - 32 lim x-2 X-2
In exercises use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. lim x-0 [1/(2 + x)]- (1/2) X
In exercises find the limit of the trigonometric function. lim tan x x- X-T
In Exercise create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. x - 2 x1x²+x-6 lim X
In exercises find the limit of the trigonometric function. lim cos x-1 TT.X 3
In exercises find the limit of the trigonometric function. lim sin x X→π/2
In exercises find the limit of the trigonometric function. lim sin x-2 Π.Χ. 2
Finding a for a Given ε The graph ofis shown in the figure. Find δ such that if 0 < |x - 2| < δ, then |ƒ(x) -1| < 0.01. f(x) = 1 x - 1
In exercises find the limit of the trigonometric function. lim cos 3x X-T
In exercises find the limit of the trigonometric function. lim sec 2x x-0
In exercises find the limit of the trigonometric function. lim sin x x-5π/6 5m
In exercises find the limit of the trigonometric function. lim cos x X-5T/3
In exercises find the limit of the trigonometric function. lim sec x→7 Π.Χ. 6
In exercises find the limit of the trigonometric function. lim tan x-3 π.Χ. 4
In exercises use the information to evaluate the limits.a.b.c.d. lim f(x) = 2 ХЭС lim g(x) = ²/ X-C (a) lim [4f(x)] X-C (b) lim [f(x) + g(x)] X-C (c) lim [f(x) g(x)] X-C (d) lim X-C f(x) g(x)
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (2x-1) x-4
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (4x + 5) x-2
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim 3 x→6
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (2x + 1) x-3
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (-1) x→2
In exercises use the information to evaluate the limits.A.B.C.D. lim f(x) = 27 X-C f(x) (a) lim X-C (b) lim x f(x) 18 (c) lim [f(x)]² X-C (d) lim [f(x)]2/3 X-C
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. x4 - 5x² lim x-0
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. x4 - 5x² lim x-0
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. lim x-0 x² + 3x X
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. x4 - 5x² lim x-0
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim 3x x-0
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim_ |x - 5] x--5
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. x4 - 5x² lim x-0
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim √x x→4
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (x² + 4x) x-4
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim |x - 3| x-3
In exercises write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. x4 - 5x² lim x-0
Write a brief description of the meaning of the notation lim f(x) = 25. x-8
In Exercise find the limit L. Then use the ε-δ definition to prove that the limit is L. lim (x² + 1) x→1
In exercises find the limit of the trigonometric function. lim x-0 3(1 - cos x) X
In exercises find the limit of the trigonometric function. sin x lim x-o 5x x→0
What is the limit of ƒ(x) = 4 as x approaches π?
In exercises find the limit of the trigonometric function. lim x-0 sin x(1 - cos x) x²
What is the limit of g (x) = x as x approaches π?

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