Question

Find k so that the function

$f\left(x\right)$=$\{1-\cos 2x$ / $2x^2$ $x\ne 0$

$\{k$ $x=0$
is coutinous at $x=0$

Answer 1

$f\left(x\right)$ is continuous at $x=0$

$⟹k=\underset{x\to 0}{lim}\frac{1-\cos 2x}{2x^2}=\underset{x\to 0}{lim}\frac{2{\sin }^{2}x}{2x^2}=\underset{x\to 0}{lim}\frac{{\sin }^{2}x}{x^2}=1$