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`

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 .

If f(x)={e^(1/x) ,1 ifx!=0ifx=0 Find whether f is continuous 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 .

If f(x)={e^(1//x),\ \ \ if\ x!=0 1,\ \ \ if\ x=0 . Find whether f 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 .

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 .

If f(x)=sin|x|-e^(|x|) then at x=0,f(x) is

Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well as differentiable at x=0 continuous but not differentiable at x=0 differentiable but not continuous at x=0 none of these

Let f(x) be a function defined on (-a ,a) with a > 0. Assume that f(x) is continuous at x=0a n d(lim)_(xvec0)(f(x)-f(k x))/x=alpha,w h e r ek in (0,1) then f^(prime)(0^+)=0 b. f^(prime)(0^-)=alpha/(1-k) c. f(x) is differentiable at x=0 d. f(x) is non-differentiable at x=0