Get Beginner Calculus Help: Solving Limit Problems with Ease

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I realize this question will probably be too easy for people who are good at it.

But I can't figure this out.

I'm trying to find the limit for

lim x→7 (sin(x − 7))/(x2 + 2x − 63)

Sorry, I don't know how to make it look like the proper equation.

Thanks for any help...
 
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welcome to PF!

now what have you tried, or what relevant equations/theorems do you know?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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