18: After substituting the limit point into the given expression you should get

Why is there 1^- in the logarithm? It is necessary to determine whether for x close to but smaller than 5 the expression (2x − 4)/(x + 1) is smaller than or greater than 1. This cannot be done by playing with pluses and minuses, since after substituting in one gets 6^-/6^- which does not help at all, all depends on a fine balance of numerator and denominator. The easiest way is to solve some algebraic inequality, for instance one can ask when is the ratio less than 1. Turns out that such an inequality is true for x between −1 and 5, which shows that as we approach 5 from the left, the ratio approaches 1 from smaller numbers and it becomes 1^-.

Hint on limit at −∞
Hint on limit at −1 from the left
Hint on limit at 2 from the right
Hint on limit at 5 from the right
Hint on limit at ∞
Answer