f-x-tan-pi-4-x-1-x-k-is-conntinous-at-x-0-then-k-

Question Number 48581 by Kiran bendkoli last updated on 25/Nov/18

f (x) = [\tan {(π / 4 + x)}^{1 / x}]

= k

i s c o n ntinous at x = 0 then k = ?

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Nov/18

i t h i n k f (x) = {[t a n (\frac{π}{4} + x)]}^{\frac{1}{x}}

f (x) = {[\frac{1 + x}{1 - x}]}^{\frac{1}{x}}

l n {f (x)} = \frac{l n (1 + x) - l n (1 - x)}{x}

l n {f (x)} = \frac{l n (1 + x)}{x} + \frac{l n (1 - x)}{- x}

\lim_{x \to 0} l n {f (x)} = \lim_{x \to 0} {\frac{l n (1 + x)}{x} + \frac{l n (1 - x)}{- x}}

= 1 + 1 = 2

s o k = e^{2}