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

lim_(xto1) (1-x^(2))/(sin2pix) is equal to

lim_(x rarr1)(1-x^(2))/(sin2 pi x) is equal to (a)(1)/(2 pi)(b)-(1)/(pi)(c)(-2)/(pi)(d) none of these

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=-(3 pi^(2))/(4) then lim_(x rarr-pi)(f(x))/(sin(sin x)) is equal to (a)0( b) pi (c) 2 pi (d) none of these

lim_(xrarr1) (1+cos pix)cot^2pi x is equal to

lim_ (x rarr1) (1-x ^ (2)) / (sin pi x)

lim_(x rarr1)(1+cos pi x)cot^(2)pi x is equal to

("lim")_(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to pi (b) 2pi (c) pi/2 (d) none of these

int_1^(e^(17))(pi"sin"(pi(log)_e x))/x dx is equal to (A) 2 (B) -2 (C) 2//pi (D) none of these

int_(0)^(oo)((pi)/(1+pi^(2)x^(2))-(1)/(1+x^(2)))log xdx is equal to (a)-(pi)/(2)ln pi(b)0(c)(pi)/(2)ln2(d) none of these

The value of lim_(x->1)(2-x)^(tan((pix)/2)) is e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)