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->0)(|sin x|)/x is a. 1 b . -1 c. 0 d. none of these

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

(lim_(x rarr0)(|s in x|)/(x) is a.1b*-1c.0d .none of these

(lim)_(x rarr oo)(|x|)/(x) is equal to a.1b*-1c.0d . none of these

Let f(x)={(sinx^2)/x x!=0 0x=0, then f^(prime)(0^+)+f^(prime)(0^-) has the value equal to (a) 0 (b) 1 (c) 2 (d) None of these

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 the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , then the value of k is (a) 0 (b) 1 (c) -1 (d) None of these

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

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

If f(x)={("sin"[x])/([x]) ,for [x]!=0, 0 ,for[x]=0,where [x] denotes the greatest integer less than or equal to x , then lim_(x→0)f(x) is (a) 1 (b) 0 (c) -1 (d) none of these