If `f(x)=(lim)_(xvecoo)(cosx/(sqrt(n)))^n` , then the value of `(lim)_(xvec0)(f(x)-1)/x` is `0` b. `1` c. 2 d. `3//2`

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

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

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

The value of ("lim")_(xvec0)(e^(2x)-cos x-"ln"(1+2x))/(xtanx-sinx)i s 0 (b) 1 (c) 2 (d) 3

If lim_(x rarr0)[1+x+(f(x))/(x)]^((1)/(x))=e^(3), then the value of ln(lim_(x rarr0)[1+(f(x))/(x)]^((1)/(x))) is

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

(lim)_(xvec0)((1-cos2x)(3+cosx)/(xtan4x) is equal to: (1) 4 (2) 3 (3) 2 (4) 1/2

If f(n)=(lim)_(xrarroo)((1+sinpi/2)(1+sinpi/(2^2))(1+sinpi/(2^n)))^(1/x) then (lim)_(nrarro)f(n)= 1 b. e c. 0 d. oo

If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2 Then the value of (lim)_(xvec0)g(f(x)) a. is -2 b. is -3 c. is 1 d. does not exist