Let lim(n->oo)((x^2+2x+3+sinpix)^n-1)/((...

Let `lim_(n->oo)((x^2+2x+3+sinpix)^n-1)/((x^2+2x+3+sinpix)^n+1)`. then

A

f(x) is continuous and differentiable for all ` x in R`

B

f(X) is continuous but not differentiable for all ` x in R`

C

f(x) is discontinuous at infinite number of points

D

f(x) is discontinuous at finite number of points

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

Let f(x)=lim_(nrarroo)((x^(2)+2x+4+sinpix^(n))-1)/((x^(2)+2x+4+sinpix^(n))+1) , then

let lim_ (n rarr oo) ((x ^ (2) + 2x + 3 + sin pi x) ^ (n) -1) / ((x ^ (2) + 2x + 3 + sin pi x) ^ (n ) +1)

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

Let f(x)=lim_(n to oo) sinx/(1+(2 sin x)^(2n)) then f is discontinuous at

Let f(x)=lim_(n rarr oo)(log(2+x)-x^(2n)sin x)/(1+x^(2n)) then

Let f(x)=lim_(n rarr oo)(2x^(2n)sin\ 1/x+x)/(1+x^(2n)) then find (a) lim_(x rarr oo) x f(x) (b) lim_(x rarr 1) f(x)