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

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

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 (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

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)={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

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

The function f(x)=|cosx| 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

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

The function f(x)=e^(|x|) is (a) Continuous everywhere but not differentiable at x = 0 (b) Continuous and differentiable everywhere (c) Not continuous at x = 0 (d) None of the above