If`g(x)=int_0^x2|t|dt`,then (a)`g(x)=x|x|` (b)`g(x)` is monotonic (c) g(x) is differentiable at x=0 (d)`gprime(x)`is differentiable at x=0

If g(x)=int_0^x2|t|dt ,t h e n (a) g(x)=x|x| (b) g(x) is monotonic (c) g(x) is differentiable at x=0 (d) g^(prime)(x) is differentiable at x=0

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)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

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 g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0 .Let f(x)={x/|x|g(x), 0 !=0 and 0,x=0 and h(x)=e^(|x|) for all x in R . Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)) . Then which of the following is (are) true? A. f is differentiable at x = 0 B. h is differentiable at x = 0 C. f o h is differentiable at x = 0 D. h o f is differentiable at x = 0

f(x) is differentiable function and (f(x).g(x)) is differentiable at x = a . Then (a) g(x) must be differentiable at x=a (b.) if g(x) is discontinuous, then f(a)=0 (c.) if f(a)!=0 , then g(x) must be differentiable (d.) none of these

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