Question

Let g be the function defined on 0, pi/2) to which the series in (a) converges. Show that g is differentiable.

Answer 1

The question focuses on proving that a function represented by a convergent power series is differentiable on a certain interval in the subject of calculus.

Step-by-step explanation:

The student's question seems to revolve around the concept of function differentiability within calculus, specifically for power series.

To show that a function g is differentiable, one must prove that the derivative of g exists within the interval (0, pi/2).

In the context of power series, if the series converges absolutely and uniformly on this interval, then the function represented by the series is differentiable there.

This is a direct consequence of term-by-term differentiation of power series within their radius of convergence.