2) Calculate the following limits (You can't use the L'Hopital's rule): a) Algebraically: $$ \lim_{x \to -1} \frac{\sqrt{x+5}-2}{x^2+6x+5} $$ $$ 3x-1 $$
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First, let's try to substitute $x = -1$ into the expression: Numerator: $$ \sqrt{-1+5}-2 = \sqrt{4}-2 = 2-2 = 0 $$ Denominator: $$ (-1)^2+6(-1)+5 = 1-6+5 = 0 $$ Since we get the indeterminate form $\frac{0}{0}$, we need to simplify the expression. Show more…
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