Which one is Bigger ?? e^(pi) or (pi)^e

Determine which is bigger, (1)/(pi)^(1/e) or (1)/(e )^((1)/(pi)) ?

Identify which is greater -(1+e^(2))/(e) or (1+pi^(2))/(pi)

Which one is greater: cos(log_(e)theta) or log_(e)(cos theta) if -(pi)/(2)

Which one is greater: cos(log_e theta)or log_e(costheta) if -pi/2ltthetaltpi/2

Prove that inequality e^(x)>(1+x) for all x in R_(0) and use it to determine which of the two numbers e^(pi) and pi' is greater.

Use the function f(x)=x^(1/x), x gt 0 , to determine the bigger of the two numbers e^(pi) and pi^(e) .

The correct option among the following is (a)pi^(e) e^(pi),(c)pi^(e)=e^(pi),(d) none of these

For the function f(x) = x^(x) , find the points at which it is (i) increasing and (ii) decreasing. Hence determine which of e^(pi), pi^(e) is greater.

If z!=0 upper bound of |z^(i)| is A) |z| B) 1 C) e^(-pi) D) e^(pi)