The value of `lim_(m->oo)(cos(x/m))^("m")` is 1 (b) e (c) `e^(-1)` (d) none of these

The value of lim_(xto oo)e^(-x) is

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_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (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

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_2 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these

The value of (lim)_(x->oo)(e^sqrt(x^(4+1))-e^(x^(2+1))) is (a) 0 b. e c. 1//e d. -oo

f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)_(xvec0)(f(x))/x is equal to 1 b. -1 c. zero d. none of these

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

lim_(xtooo)(1+k/x)^(m/x)

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