25: This general power needs to be transformed into its canonical form first:

Conditions
    • arcsin[(x + 2)/(x − 1)] > 0,
    • −1 ≤ (x + 2)/(x − 1) ≤ 1,
    • x − 1 ≠ 0,
    • x + 5 ≠ 0
give the domain

D( f ) = (−∞,−5) ∪ (−5,−2).

Now it is time to find limits at −∞, at −5 from the left and from the right, and at −2 from the left.

Hint on limit at −∞
Hint on limit at −5 from the left
Hint on limit at −5 from the right
Hint on limit at −2 from the left
Answer