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-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

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)=|(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

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 : 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)=|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

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)= ((xe^(-1/|x|+1/x), if, x!=0),(0 , if, x=0)) , then f(x) is 1) continuous for all x, but is not differentiable2) neither differentiable nor continuous3) discontinuous everywhere4) continuous as well as differentiable for all x