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

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

If g(x)=int_(0)^(x)cos^(4)t dt , then prove that g(x+pi)=g(x)+g(pi) .

If g(x)=int_(0)^(x)cos^(4) t dt , then (x+pi) equals

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Differentiate x^(sin x), x gt 0 w.r.t. x.

Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x),g^(prime)(x) be a , b , respectively, (a

Let g(x) = x^2+ sin x. Calculate the differential dg.

Let f(x)a n dg(x) be two functions which are defined and differentiable for all xgeqx_0dot If f(x_0)=g(x_0)a n df^(prime)(x)>g^(prime)(x) for all x > x_0, then prove that f(x)>g(x) for all x > x_0dot

if f(x) =ax +b and g(x) = cx +d , then f[g(x) ] - g[f(x) ] is equivalent to