If f(x)={(1-cosx)/(x^2)\ \ \ ,\ \ \ x!=0...

If `f(x)={(1-cosx)/(x^2)\ \ \ ,\ \ \ x!=0k\ \ \ ,\ \ \ x=0` is continuous at `x=0` , find `kdot`

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Verified by Experts

For f to be continuous `f(0)=lim_(x→0)f(x)`
`k=lim_(x→0)(1−cosx)/x`
`=lim_(x→0) (2sin^2(x/2))/(x/2)^2⋅(x/4)=1/2⋅0=0`

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