The value of $\underset{x→1}{\lim}\

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

The value of $\underset{x→1}{\lim}\cos^{-1}(\log_4\frac{x}{4})$

Options:

equals $-\frac{π}{2}$

$\frac{π}{2}$

does not exist

Correct Answer:

does not exist

Explanation:

$\underset{x→1}{\lim}\cos^{-1}(\log_4 x-1)$

but x = 1 - h, $(\log_4 x)$ is negative.

So, $\cos^{-1}(\log_4 x-1)$ is not defined for x = 1 - h.