The function f defined by `f(x)=lim_(t->oo) {((1+sinpix)^t-1)/((1+sinpix)^t+1)}` is

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

Is the function f defined by f(x)={{:(x , ifxlt=1),( 5, ifx >1):} continuous at x = 0? A t x = 1? A t x = 2?

If quad f(x)=lim_(t rarr oo)((| alpha+sin pi x|)^(t)-1)/((| alpha+sin pi x|)^(t)+1),x in(0,6)

If f(x)=lim_(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))] ,then f(1) is …….

If f(x)=lim_(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))] ,then f(1) is …….

If f(x)=lim_(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))] ,then f(1) is …….

If f(x)=lim_(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))] ,then f(1) is …….

If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^(-1) is