💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

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

Discussion

You must be signed in to discuss.

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.