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 .

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 .

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)=(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

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 .

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

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 .

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

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)

Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e"[dot] represents greatest integer function, is discontinuous at x=0,t h e nh(x)=f(x)dotg(x) is discontinuous at x=0. Statement 2: If f(x) is continous and g(x) is discontinuous at x=a ,t h e nh(x)=f(x)g(x) is discontinuous at x=a