Question

For what value of is continous where f(a) f 1- cose function flu) , nto 22 K2=0

11th - 12th Class

Maths

Solution

354

4.0 (1 ratings)

( f(x)=left{begin{array}{cc}frac{1-cos x}{x^{2}} & , x eq 0 k & , x=0end{array}right. ) ( frac{L H L}{x rightarrow 0^{-}}left(frac{1-cos x}{x^{2}}right)=lim _{h rightarrow 0} frac{1-cos h}{h^{2}} ) ( =operatorname{li}_{h rightarrow 0} frac{2 sin ^{2}left(frac{h}{2}right)}{frac{h^{2}}{4} cdot 4}=frac{2}{4}=frac{1}{2} ) ( ln 2=lim _{h rightarrow 0} frac{1-cos h}{h^{2}}=frac{1}{2} ) ( f(x) ) is coutiutom 2) ( f(x)(text { at } x=0)=L H L=R H L ) ( Rightarrow quad k=frac{1}{2} )