A function is defined as f(x)=lim(x->oo)...

A function is defined as `f(x)=lim_(x->oo)[cos^(2n) x` , if `x<0)` , `nsqrt(sqrt(1+x^n,` if `0<=x,+1)` , `1/(1+x^n),` if `x>1` which of the following does not hold good?

A

continuous at x=0 but discontinuous at x=1

B

continuous at x=1 but discontinuous at x=0

C

continuous both as x=1 and x=0

D

discontinuous both at x=1 and x=0

Verified by Experts

The correct Answer is:

A, B, C

Similar Questions

Explore conceptually related problems

A function is defined as f(x)=lim_(x rarr oo)[cos^(2n)x, if x 1 which of the following does not hold good?

The function defined as f(x)=lim_(n rarr oo){cos^(2n)x if x which of the following is correct

A function fis defined by f(x)=int_(0)^( pi)cos t cos(x-t)dt,0<=x<=2 pi then which of the following.hold(s) good?

Consider the function f(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^(2)-a)/(x^(2)+a), agt0 which of the following is not true?

A differentiable function satisfies f(x)=int_(0)^(x){f(t)cost-cos(t-x)}dt. Which is of the following hold good?

Let f:(-pi/2, pi/2)->R, f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N; 1 if x=0 which of the following holds good?

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

Discuss the continuity of f(x)=lim_(n rarr oo)cos^(2n)x

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1);0

Let f : R to R be a function such that lim_(x to oo) f(x) = M gt 0 . Then which of the following is false?