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

Show that f(x) =x^(3) is continuous as well as differentiable at x=3

The function f(x)=|x|+|x-1| is Continuous at x=1, but not differentiable at x=1 Both continuous and differentiable at x=1 Not continuous at x=1 Not differentiable at x=1

If f(x)=|ln|x|, then (a)f(x) is continuous and differentiable for all x in its domain (b) f(x) is continuous for all 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

If f(x)=|(log)_e|x| , then 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

If f(x)={(1)/(1+e^(1/x)),quad x!=00,quad x=0 then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

The function f(x)- Icos xl is (a) everywhere continuous and differentiable b) everywhere continuous but not differentiable at (2n t 1) n/2,ne Z (c) neither continuous nor differentiable at (2n + 1)n/2,ne Z (d) none of these

If f(x)={(1-cos x)/(x sin x),x!=0 and (1)/(2),x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (continuous but not differentiable (d)neither continuous nor differentiable

If f(x)={s in(cos^(-1)x)+cos(sin^(-1)x),xlt=0s in(cos^(-1)x)-cos(sin^(-1)x ,x >0) . Then at x=0 f(x) is continuous and differentiable f(x) is continuous but not differentiable f(x) not continuous but differentiable f(x) is neither continuous nor differentiable

The function f(x)=|cos x| is (a) everywhere continuous and differentiable (b) everywhere continuous but not differentiable at (2n+1)pi/2,n in Z(c) neither continuous nor differentiable at (2n+1)pi/2,n in Z(d) none of these

The function f(x)=|cos sx| is everywhere continuous and differentiable everywhere continuous but not differentiable at (2n+1)(pi)/(2),n in Z .neither continuous not differentiable at (2x+1)(pi)/(2),n in Z