If `f(x)=|(log)_e|x||` , then (a)`f(x)` is continuous and differentiable for all `x` in its domain] (b) `f(x)` is continuous for all `x` in its domain but not differentiable at `x=+-1` (c) `f(x)` is neither continuous nor differentiable at `x=+-1` (d) none of these

Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

Show that f(x)=|x-3| is continuous but not differentiable at x=3.

Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

Show that f(x) = |x-5| is continuous but not differentiable at x = 5 .

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

The function f : R rarr R given by f(x) = - |x-1| is (a) continuous as well as differentiable at x = 1 (b) not continuous but differentiable at x = 1 (c) continous but not differentiable at x = 1 (d) neither continous nor differentiable at x = 1

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is (a) f is continuous and differentiable for all x (b) f is continuous but not differentiable at x=0 (c) f is continuous and differentiable for all x . (d) f ' is continuous but not differentiable at x=0

f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):} (a) continuous and differentiable at x=1 (b) continuous but not differentiable at x=1 (c) neither continuous nor differentiable at x=1 (d) none of these

Let f(x)={1, x =1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable