- #1

Robultronic

- 5

- 0

## Homework Statement

Given f : [-[tex]\sqrt{\pi}[/tex], [tex]\sqrt{\pi}[/tex] ] [tex]\rightarrow[/tex] [-1, 1]

f(x) = sin(x[tex]^{2}[/tex])

a)

Show that f is continuous for all a [tex]\in[/tex] [-[tex]\sqrt{\pi}[/tex], [tex]\sqrt{\pi}[/tex] ]

b)

Find a [tex]\delta[/tex] so that |x - y| [tex]\leq[/tex] [tex]\delta[/tex] implies that

|f(x) - f(y)| [tex]\leq[/tex] 0.1 for all x and y in [-[tex]\sqrt{\pi}[/tex], [tex]\sqrt{\pi}[/tex] ]

## Homework Equations

## The Attempt at a Solution

I honestly don't know where to begin. But would be very pleased for any help. A full solution would be the optimal though. But anything helps.