`("lim")_(xvec1)[cos e c(pix)/2]^(1/((1-x)))(w h e r e[dot]r e p r e s e n t st h e` `gif is e q u a l to`(a) 0 (b) 1 (c) `oo` (d) does not exist

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a)-1 (b) 1 (c) 0 (d) does not exist

lim_(x->0)|x(x-1)|^[cos2x] ; where [.] is GIF is equal to : A.) 1 B.) 0 C.) e D.) does not exist

The minimum value of x(log)_(e)x is equal to e (b) 1/e(c)-1/e (d) 2e( e )e

(lim)_(x->oo)(logx^n-[x])/([x]),\ n in N ,\ ([x]\ d e not e s\ t h e\ in t ege r\ l e s stanor\ e q u a l\ to\ x)\

If L=(lim)_(x->oo)(logx^n-[x])/([x]),\ w h e r e\ n in N ,\ t h e n-2L=

In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respectively, in the ratio k :1(inor d e r)dot If the ratio ((a r E A P Q R)/(a r e a A B C)) IS 1/3,t h e nk is equal to 1/3 (b) 2 (c) 3 (d) none of these

(lim_(x rarr oo)((1)/(e)-(x)/(1+x))^(x) is equal to (a)(e)/(1-e)(b)0(c)(e)/(e^(1-e))(d) does not exist

If f(x)={("sin"[x])/([x]),for[x]!=0 0,for[x]=0,w h e r e[x] denotes the greatest integer less than or equal to x , then ("lim")_(xvec0)f(x) is 1 (b) 0 (c) -1 (d) none of these

Show that lim_(xto0^(-)) ((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

int_(-(pi)/(2))^((pi)/(2))(e^(|sin x|)cos x)/(1+e^(tan x))dx is equal to (a) e+1 (b) 1-(pi)/(2)e(c)e-1(d) none of these