1.

Let f(x)={(lim_(nto oo) ((px)/n sum_(r=1)^(n) ([r^(2)-e^(-x)+r-1])/(r(r+1)))+lamda,xgt0),(q, x=0),(lim_(nto oo) sum_(r=1)^(n) ({r^(2)+r+e^(x)-1})/(r(r+1)), xlt0):} Is differentiable is R: ([.] is G.I.f and {.} is F.P. of x) Then,

Answer»

`p=1`
`q=1`
`p+q+lamda=3`
if `g` is inverse of `F` then `g^(')(1//2)=2`

Solution :abcd
`f(x)={(px+lamda, XGT0),(q,x=0),(E^(x),XLT0):}`


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