Let `g\ :[1,6]->[0,\ )` be a real valued differentiable function satisfying `g^(prime)(x)=2/(x+g(x))` and `g(1)=0,` then the maximum value of `g` cannot exceed `ln2` (b) `ln6` `6ln2` (d) `2\ ln\ 6`

Let g:[1,6]rarr[0,) be a real valued differentiable function satisfying g'(x)=(2)/(x+g(x)) and g(1)=0, then the maximum value of g cannot exceed ln2(b)ln6 6ln2(d)2ln6

Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x) and g (0)=1 , then g(x)((2-sin2x)/(1-cos2x))dx is equal to

Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x) and g (0)=1 , then intg(x)((2-sin2x)/(1-cos2x))dx is equal to

Suppose g(x) is a real valued differentiable function satisfying g'(x) + 2g(x) gt 1. Then show that e^(2x)(g(x)-1/2) is an increasing function.

Suppose g(x) is a real valued differentiable function satisfying g'(x)+2g(x)>1. Then show that e^(2x)(g(x)-(1)/(2)) is an increasing function.

Let the function g be defined by g(x)=5x+2 . If sqrt(g((a)/(2)))=6 , what is the value of a?

Let f(x)and g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 , g'(1)=6 , f(2)=3 and g(2)=9 . Then what is f(x)-g(x) at x=4 equal to ?

If (log)_(x)a,a^(x/2) and (log)_(b)x are in G.P.then write the value of x.

Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2