If `f(x)=x s in(1//x), x!=0` then `(lim)_(x->0)f(x)=` a. 1 b . -1 c. 0 d. does not exist

If f(x)=xs in(1/x),x!=0 then (lim_(x rarr0)f(x)= a.1b*-1 c.0 d.does not exist

If f(x)={xsin(1/x) ,\ x!=0, then (lim)_(x->0)f(x) equals a. 1 b . 0 c. -1 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

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

(lim)_(x rarr oo)(sin x)/(x) equals a.1b*0c.oo d . does not exist

If f(x)={((tan^-1(x+[x]))/([x]-2x)[x]ne0,,),(0[x]=0,,):} where [x] denotes the greatest integer less than or equal to x, than lim_(xto0) f(x) is (a) (-1)/2 (b) 1 (c) (pi)/4 (d) Does not exist