(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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] ]

2. Relevant equations

3. 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.

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# Homework Help: Show that f(x) = sin(x^2) is continuous for all a [-sqrt(pi), sqrt(pi).

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