If f(x) = {[(36^x-9^x-4^x+1)/√2-√(1+cosx) ,x≠0][k,x=0] is continuous at x = 0, then k equals. A. 16 log 2 log 3 B. 16 In 6 ​

Question

If \(f(x) = \begin{cases} \frac{36^x-9^x-4^x+1}{\sqrt{2}-\sqrt{1+cosx}}&, \quad x ≠{0}\\ k &, \quad x={ 0} \end{cases} \) is continuous at x = 0, then k equals.

A. 16\(\sqrt{2}\) log 2 log 3

B. 16\(\sqrt{2}\) In 6

C. 16\(\sqrt{2}\) In 2 In 3

D. none of these

Answer 1

Option : (c)

(i) A function f(x) is said to be continuous at a point x = a of its domain, if  \(\lim\limits_{x \to a}f(x)=f(a)\) 

Given :-

\(f(x) = \begin{cases} \frac{36^x-9^x-4^x+1}{\sqrt{2}-\sqrt{1+cosx}}&, \quad x ≠{0}\\ k &, \quad x={ 0} \end{cases} \) 

Function f(x) is continuous at x = 0

\(\lim\limits_{x \to 0}f(x)=f(0)\)