If the functions `f(x)` , defined below is continuous at `x=0` , find the value of `k :` `f(x)={(1-cos2x)/(2x^2)\ \ \ ,\ \ \ x<0k\ \ \ ,\ \ \ x=0,x/(|x|)\ \ \ ,\ \ \ x >0`

Explanation

Given, f(x) is continuous at `x=0`

`⇒lim_(x→0)​f(x)=f(0)=k`

Again,

`lim​_(x→0+)f(x)=lim​_(x→0+)=x/(∣x∣)​=1`


And,


`=>lim_(x→0−)​f(x)=lim_(x→0−)​(1−cos2x)/(2x^2)​`

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