Question

Find an equivalent expression for the limit as x approaches pi of the quantity sin x minus sin pi close quantity over the quantity x minus pi question mark

B .cosπ
C. sinx − sinπ

Choose either B or C. The other two answers I have confirmed as incorrect.

Answer 1

C. sinx - sinπ

Explanation:

The expression in the question asks for an equivalent expression for the limit as x approaches pi of the quantity (sin x - sin pi) / (x - pi). To find an equivalent expression, we can simplify the given expression using the fact that sin(pi) = 0.

Let's simplify the expression step by step:

1. Start with the given expression: (sin x - sin pi) / (x - pi)

2. Substitute sin(pi) with 0: (sin x - 0) / (x - pi)

3. Simplify further: sin x / (x - pi)

So, an equivalent expression for the given limit is sin x / (x - pi).

Therefore, the correct option is C. sin x − sin π.