The value of undersetx→1limcos^-1(log_4x/4)

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

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

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