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

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

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

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

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

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)=|(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

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

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

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