`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)=|cosx x 1 2sinx x2xsinx x x| , then (lim)_(x->0)(f(x))/(x^2) is equal to (a) 0 (b) -1 (c) 2 (d) 3

The value of lim_(x rarr0)(sqrt((1)/(2)(1-cos2x)))/(x) is (a) 1(b)-1(c)0(d)none of these

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

f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The value of underset(x rarr 0)(lim) (f(x))/(x) is equal to

The value of (lim)x rarr0(sqrt(1-cos x^(2)))/(1-cos x) is a.(1)/(2) b.2 c.sqrt(2)d .none of these

If f(x)={xsin1/x , x!=0 0, x=0 , then (lim)_(x->0)f(x) equals a. 1 b . 0 c. -1 d. none of these

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

Let f(x)=2x^(1//3)+3x^(1//2)+1. The value of lim_(hrarr0)(f(1+h)-f(1-h))/(h^(2)+2h) is equal to

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

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