Discussion Forum

If f(x) = $\frac{e^{x^{2}}-\cos x}{x^{2}}$  , for x≠ o, is continuous  at x=0, then of f(0) is

Answer:

Explanation:

We have,

f(x) = $\frac{e^{x^{2}}-\cos x}{x^{2}}$   is continuous at x=0

 $\therefore$     $\lim_{x \rightarrow 0}f(x)=f(0)$

 $\Rightarrow$   $f(0)=\lim_{x \rightarrow0}\frac{e^{x^{2}}-\cos x}{x^{2}}$

 $\Rightarrow$    $f(0)=\lim_{x \rightarrow0}\frac{2xe^{x^{2}}+\sin x}{2x}$

                                    [ apply L' Hosptial rule]

 $\Rightarrow$    $f(0)=\lim_{x \rightarrow0}\frac{2xe^{x^{2}}}{2x}+\lim_{x \rightarrow 0}\frac{\sin x}{2x}=1+\frac{1}{2}=\frac{3}{2}$