" (i) "phi(e^(x))=x

Let inte^(x){f(x)-f'(x)}dx=phi(x) . Then inte^(x)*f(x)dx is a) phi(x)+e^(x)f(x) b) phi(x)-e^(x)f(x) c) 1/2{phi(x)+e^(x)f(x)} d) 1/2{phi(x)+e^(x)f'(x)}

If phi(x)=log_ex , then show: phi(e^x)=x

Show that each of the following functions is strictly increasing phi (x)=e^(x)

If the function f(x) and phi (x) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of functions f(x) = e^(x), phi (x) = e^(-x) is

Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(x)|=|f(x)|+|phi(x)| are :

Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(x)|=|f(x)|+|phi(x)| are :

If phi(x) is a differentiable function, then the solution of the different equation dy+{y phi' (x) - phi (x) phi'(x)} dx=0, is

If phi(x) is a differentiable function, then the solution of the different equation dy+{y phi' (x) - phi (x) phi'(x)} dx=0, is