`(lim)_(xvecoo)x^2sin((log)_esqrt(cospi/x))` a. 0 b. `(pi^2)/2` c. `(pi^2)/4` d. `(pi^2)/8`

The value of the integral int_(pi//2)^(pi//2)(x^2ln(pi+x)/(pi-x))cosx\ dx is a. 0 b. (pi^2)/2-4 c. (pi^2)/2+4 d. (pi^2)/2

The value of (lim)_(x->pi/2)(int t\ dt)/(sin(2x-pi)) integral from pi/2 to x is oo b. pi/2 c. pi/4 d. pi/8

lim_(x rarr(pi)/(2))((1-sin x)(8x^(3)-pi^(3))cos x)/((pi-2x)^(4))-(pi^(2))/(6) b.(3 pi^(2))/(16) c.(pi^(2))/(16)d .-(3 pi^(2))/(16)

int_(0)^( pi)(x tan x)/(sec x+cos x)dx is (pi^(2))/(4)(b)(pi^(2))/(2)(c)(3 pi^(2))/(2) (d) (pi^(2))/(3)

(lim)_(x->1)(1-x)tan((pix)/2)\ a. pi/2 b. pi c. 2/pi d. 0

The smallest positive x satisfying the equation log_(cos x)sin x+log_(sin x)cos x=2 is (pi)/(2)(b)(pi)/(3)(c)(pi)/(4)(d)(pi)/(6)

lim_ (x rarr0) sin ^ (2) ((pi) / (2-px)) ^ (sec ^ (2) (((pi) / (2-4 pi))))

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

("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