If `G(x)=-sqrt(25-x^2),t h e n lim_(x->1)(G(x)-G(1))/(x-1)i s` (a)`1/(24)` (b) `1/5` (c) `-sqrt(24)` (d) none of these

Compute lim_(x to 1) (sqrt(x)-1)/(x-1)

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

The value of lim_(x->0)(sqrt(1/2(1-cos2x)))/x i s (a)1 (b) -1 (c) 0 (d) none of these

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

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4

("lim")_(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(x)+...+nsqrt(n))/(sqrt((2x-3))+(sqrt(2x-3))+....+(sqrt(2x-3)) i se q u al to 1 (b) oo (c) sqrt(2) (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these