`Iff(x)={(1-cosk x)/(xsinx),x!=0 1/2,x=0i s con t inuou sa tx=0,fin dkdot`

Explanation

Since `f(x)` is continuous at `x=0`, so



`lim _{x => 0} f(x)=f(0)=frac{1}{2}`


`lim _{x => 0} f(x)=frac{1}{2}`


`lim _{x => 0}(frac{1-cos k x}{x sin x})=frac{1}{2} `


`lim _{x => 0}(frac{k sin (k x)}{sin x+x cos x})=frac{1}{2}`




...