The function f defined by `f(x)=lim_(t->oo) {((1+sinpix)^t-1)/((1+sinpix)^t+1)}` is
(A) everywhere continuous
(B) discontinuous at all integer values of x
(C) continuous at x = 0
(D) none of these

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

Let [.] denotes G.LP. for the function f(x)=(tan (pi[x-pi])/(1+[x]^2)) the wrong statement is (A) f(x) is discontinuous at x=0 (B) f(x) is continuous for all values of x (C) f(x) is continuous at x=0 (D) f(x) is a constant function

The function f(x)=sin^(-1)(cos x) is discontinuous at x=0 (b) continuous at x=0( c) differentiable at x=0 (d) none of these

The function f(x)=sin^(-1)(cosx) is (a) discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

1.If lim_(x rarr0)(f(x))/(x) exists and f(0)=0 then f(x) is (a) continuous at x=0 (b) discontinuous at x=0 (e) continuous no where (d) None of these

The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0, at x=0 ,f(x)=0 a. is continuous at x=0 b. is not continuous at x=0 c. is not continuous at x=0, but can be made continuous at x=0 (d) none of these

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

The function f(x)=e^(|x|) is (a) Continuous everywhere but not differentiable at x = 0 (b) Continuous and differentiable everywhere (c) Not continuous at x = 0 (d) None of the above