Question

Estimate the limit A B C D

Answer 1

Answer:

C. $\lim_{x\rightarrow f(x)=2$

Step-by-step explanation:

Given problem is $\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}$.

Now we need to evaluate the given limit.

If we plug $\x=\frac{\pi}{4}$, into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

$\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}$

$=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}$

$=\frac{sec^2(\frac{\pi}{4})-0}{1-0}$

$=\frac{(\sqrt{2})^2}{1}$

$=\frac{2}{1}$

=2

Hence choice C is correct.