Is the following function continuous: f(x)={x^2+sin(5x) for x pi Please show step by step work!

Question

Is the following function continuous:

f(x)={x^2+sin(5x) for x< or equal to pi
        {-x-cos(x/2) for x> pi

Please show step by step work!

goformit100 · Answer

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anonymous · Answer

I think I know the answer:
Lim x--> pi- x^2+sin(-5x) = limx-->pi- x^2 + limx-->pi- sin(-5x) = pi^2 +0=pi^2
Lim x-->pi+ -x-cos(x/2)= lim x--> pi+ -x -limx-->pi+ cos(x/2)=-pi-0=-pi
-pi does not = pi^2, so it's not continuous since the one sided limits are approaching different values

anonymous · Answer

Yes, that's right there is a jump discontinuity where the first piecewise function ends and the second one starts.

anonymous · Answer

*I mean the first part of the piecewise function.