`("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1)` is equal to (a) 0 (b) 1 (c) `1/3` (d) `1/2`

("lim")_(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c) 1 (d) -1

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

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

lim_(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 (b) 24 (c) 32 (d) 8

(lim)_(xvec0)((sqrt(1+x sin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c. 3 d. 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))

lim_(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x .

cos 4x =1- 8 sin ^(2) x cos ^(2) x

int_(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 (D) 6