Question

How do you evaluate `lim_(x->1)` `(sin(7pix))/(sin(8pix))`?

Answer 1

The initial form is the indeterminate `0/0`.

Explanation:

There might be a way to evaluate using algebra, but it's not obvious how to do that.

Let's use l"Hospital's Rule.

`lim_(x->1) (sin(7pix))/(sin(8pix)) = lim_(x->1) (7pi cos(7pix))/(8 pi cos(8pix))`

`= (7 pi cos(7pi))/(8 pi cos(8pi))`

`= (7 (-1))/(8 (1)) = -7/8`