Let f(x)={1, x <= -1, |x|, -1 < x < 1, 0, x >=1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable

Leg f(x)=|x|,g(x)=sin xa n dh(x)=g(x)f(g(x)) then h(x) is continuous but not differentiable at x=0 h(x) is continuous and differentiable everywhere h(x) is continuous everywhere and differentiable only at x=0 all of these

Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. (b) f(x) is everywhere continuous but not differentiable at x=n\ pi,\ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)pi/2 , n in Z . (d) none of these

Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x=npi,\ \ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)\ pi/2,\ \ n in Z (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)=|3-x|+[3+x] , where [x] denotes the least integer greater than or equal to x , then f(x) is:(a) continuous and differentiable at x=3. (b) continuous but not differentiable at x=3. (c)differentiable but not continuous at x=3. (d)neither differentiable nor continuous at x=3..

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)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] and differentiable on (-1, 1) (b) continuous on [-1, 1] and differentiable on ( − 1 , 0 ) ∪ ( 0 , 1 ) (c) continuous and differentiable on [-1, 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

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.

If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well as differentiable at x=0 continuous but not differentiable at x=0 differentiable but not continuous at x=0 none of these