Explanation

Given:

Expression: lim x -> 1 5 * (2x + 3) ^ -1

1. Substitute x = 1 into the expression:

lim x -> 1 5 * (2x + 3) ^ -1

= 5 * (2(1) + 3) ^ -1

= 5 * (2 + 3) ^ -1

= 5 * (5) ^ -1

2. Simplify the expression:

To simplify, we can rewrite (5) ^ -1 as 1/5.

5 * (5) ^ -1

= 5 * 1/5

= 1

Therefore, the limit of the given expression as x approaches 1 is 1.