1.

"Let"f(x)=Lim_(ntooo) ((x^(2)+4x+5+e^(x)+sgn(e^(-x)))^(n)-5)/(2(x^(2)+4x+5+e^(x)+sgn(e^(-x)))^(n)+9)then

Answer»

f(x) is DISCONTINUOUS at x=0.
f(x) is discontinuous at INFINITE number of points.
f(x) is continuous but non-derivable for all `x in R`.
f(x) is continuous and derivable for `x inR`.

Solution :`"As,"x^(2)+4x+5+e^(x)+"sgn"(e^(-x))=(x+2)^(2)+2+e^(x)gt2`.
`"So,"f(x)=(1)/(2)AAX in R`.


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