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If f(x)={(a+(sin[x])/x, , , xgt0),(b+[(s...

If `f(x)={(a+(sin[x])/x, , , xgt0),(b+[(sinx-x)/(x^(3))], , , x lt0):}`
`f(x) ` is continuous at x=0 and `b-a=k`, then evaluate k

Text Solution

Verified by Experts

The correct Answer is:
5
`f(0^+) =a ` as sin[x] = 0 as `x to 0`
`f(0^-) = b-1 ` as `(sinx -x)/(x^3) = -(1)/6 + x/(4!) - (x^2)/(5!)+ …….`
`f(0)=2 implies a=2 , b=3`
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