1.

If f(x) = {{:(a+ (sin[x])/(x) ,"," x gt 0),(2,"," x=0 ),(b+[(sinx - x)/(x^3)],"," x gt 0):} , (where [.] denotes the greatest integer function).

Answer»


SOLUTION :`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 impliesa=2 , b=3`


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