This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive Tutorial Exercise Use L'Hôpital's Rule to evaluate the limit, or state that L'Hôpital's Rule does not apply. 3x lim x-0 sin x - x Step 1 of 7 L'Hôpital's Rule states that for functions f(x) and g(x) that are differentiable on an open interval containing x = a, and if fa) = g(a) = 0, then = lim flx) X-a g'(x) if the limit on the right exists or is infinite. lim f x-a g(x) To determine whether L'Hôpital's Rule applies to the given problem, evaluate both the numerator and denominator at x = 0. At x = 0, 3x = At x = 0, sin x - x = Thus at x = 0, is sin x - x v an indeterminate form, and since both the numerator and Snot v differentiable on an open interval containing x = 0, L'Hôpital's Rule does denominatorare not аpply. are Jaes not Submit Skip (you cannot come back)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Tutorial Exercise
Use L'Hôpital's Rule to evaluate the limit, or state that L'Hôpital's Rule does not apply.
3x
lim
x-0 sin x - x
Step 1 of 7
L'Hôpital's Rule states that for functions f(x) and g(x) that are differentiable on an open interval containing
x = a, and if fa) = g(a) = 0, then
= lim flx)
X-a g'(x)
if the limit on the right exists or is infinite.
lim f
x-a g(x)
To determine whether L'Hôpital's Rule applies to the given problem, evaluate both the numerator and
denominator at x = 0.
At x = 0, 3x =
At x = 0, sin x - x =
Thus at x = 0,
is
sin x - x
3x2
v an indeterminate form, and since both the numerator and
Snot
v differentiable on an open interval containing x = 0, L'Hôpital's Rule does
denominator are not
аpply.
are
Jaes not
Submit
Skip_(you cannot come back)
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive Tutorial Exercise Use L'Hôpital's Rule to evaluate the limit, or state that L'Hôpital's Rule does not apply. 3x lim x-0 sin x - x Step 1 of 7 L'Hôpital's Rule states that for functions f(x) and g(x) that are differentiable on an open interval containing x = a, and if fa) = g(a) = 0, then = lim flx) X-a g'(x) if the limit on the right exists or is infinite. lim f x-a g(x) To determine whether L'Hôpital's Rule applies to the given problem, evaluate both the numerator and denominator at x = 0. At x = 0, 3x = At x = 0, sin x - x = Thus at x = 0, is sin x - x 3x2 v an indeterminate form, and since both the numerator and Snot v differentiable on an open interval containing x = 0, L'Hôpital's Rule does denominator are not аpply. are Jaes not Submit Skip_(you cannot come back)
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