Show that `f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0` `\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \2,\ \ \ w h e n\ x=0` is discontinuous at `x=0` .

Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \,\ \ \ w h e n\ x=a is discontinuous at x=a for any value of f(a)

Show that the function f(x)={x \ sin \ 1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ 0, when \ \ \ x=0 is continuous but not differentiable at x=0 .

If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find whether f(x) is continuous at x=0 .

Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 ; 1,\ \ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

Find the values of k for which f(x)={(1-cos4x)/(8x^2),\ \ \ w h e n\ x!=0k ,\ \ \ w h e n\ x=0 is continuous at x=0 .

Find the value of x^3+7x^2-x+1,\ w h e n\ x=1+2idot

If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) is continuous at x=0

E v a l u a t e\ (3. 2 x^6y^3)xx(2. 1 x^2y^2)w h e n\ x=1\ a n d\ y=0. 5

Evaluate ("lim")_(x->0)f(x),\ w h e r e\ f(x)={(|x|)/x ,\ x!=0 , 0,\ x=0