`(lim)_(xrarr0)(sin(picos^2x)/(x^2))` is equal to (a) `-pi` (b) `pi` (c) `pi/2` (d) 1

lim_(xrarr0)(xe^x -sin2x)/x is :

Find lim_(xrarr0)(xe^x -sin2x)/(2x)

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx is equal to (a) -pi/2lnpi (b) 0 (c) pi/2ln2 (d) none of these

Evaluate lim_(xto0) sin(picos^(2)x)/(x^(2)).

lim_(x->oo) (e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -1 (c) 1/2 (d) -1/2

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

int_(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi)/3 (c) (5pi)/6 (d) pi/3

lim_(xto pi)(sin3x)/(sin2x)

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these