Let `f(x)={(-1, -2lexlt0),(x^2-1,0lexlt2):}` if `g(x)=|f(x)|+f(|x|)` then `g(x)` in `(-2,2)` (A) not continuous (B) not differential at one point (C) differential at all points (D) not differential at two points

Let f(x)={(-,1, -2lexlt0),(x^2,-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) is (A) not continuous is (B) not differential at one point (C) differential at all points (D) not differential at two points

Let f(x)={{:(1+(2x)/(a)", "0lexlt1),(ax", "1lexlt2):}."If" lim_(xto1) "f(x) exists, then a is "

Let f(x)=|x| and g(x)=|x^3| , then (a). f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

Let f(x)=|x| and g(x)=|x^3|, then (a) f(x)a n dg(x) both are continuous at x=0 (b) f(x)a n dg(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

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

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

Let f (x)= [{:(x+1,,, x lt0),((x-1),,, x ge0):}and g (x)=[{:(x+1,,, x lt 0),((x-1)^(2),,, x ge0):} then the number of points where g (f(x)) is not 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) ={{:( 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