If f(x) = {[(1-cosx)/x^2,x≠0][k,x=0] is continuous at x = 0, find k.

Question

If \(f(x) = \begin{cases} \frac{1-cosx}{x^2} ,& x ≠{0}\\ k, & x={ 0} \end{cases} \) is continuous at x = 0, find k.

Answer 1

(i)  \(\lim\limits_{x \to 0}\frac{sinx}{x}\) = 1

(ii) 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) 

\(f(x) = \begin{cases} \frac{1-cosx}{x^2} ,& x ≠{0}\\ k, & x={ 0} \end{cases} \)

Now,