Problem

Find the limit. Use l'Hospital's Rule where appro…

01:46

Problem 29 Medium Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to 0} \frac{\tanh x}{\tan x} $

Answer

This limit has the form $\frac{0}{0} . \lim _{x \rightarrow 0} \frac{\tanh x}{\tan x}=\lim _{x \rightarrow 0} \frac{\operatorname{sech}^{2} x}{\sec ^{2} x}=\frac{\operatorname{sech}^{2} 0}{\sec ^{2} 0}=\frac{1}{1}=1$

More Answers

03:44

Mengsha Y.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

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Video Transcript

So for this problem we're wanting to use little petals role. Um and we're given tangent Hx over kanji max. This is the graph. We see that when we plug in zero though we get 0/0, which is an indeterminant form. So we're gonna want to apply look towels rule. And we see that when we take the derivative of the numerator, we get second H. X squared. Um let's actually put the squared and here And then the nominator is just going to give us 2nd squared of X. So based on this, we can now plug in zero. And we see that Seeking. H0 is going to give us one and then seeking squared of X is going to give us one. So 1/1, which is one will be our final answer for a woman.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University