Plot the graph of the function `f(x)=lim_(t->0)((2x)/pitan^(- 1)x/(t^2))`

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

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 …….

The graph of the function f(x) = underset( t rarr 0 ) ("Lim") ((2x)/(pi ) cot^(-1) ""(x) /(t^(2))) , is

The interval in which the function f(x)=int_(0)^(x) ((t)/(t+2)-1/t)dt will be non- increasing is

Find the derivative with respect to x of the following functions : (a) F(x) = int_(0)^(2x) (sin t)/(t) dt , (b) f(x) = int_(x)^(0) sqrt(1 + t^(4)) dt

If the graph of the function y=f(x) has a unique tangent at point (e^(a),0) (not vertical, non-horizontal) on the graph, then evaluate lim_(xtoe^(a))((1 +9f(x))-"tan"(f(x)))/(2f(x)) .

If the function f(x) satisfies lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi , then lim_(x to 1)f(x) is equal to