Answered: Prove that lim -- (x + 1)

Math

Calculus

Prove that lim -- (x + 1)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 1E

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Question

Expert Solution

Step 1

we have to prove that:

$\lim_{x \to - 1^{-}} \frac{5}{{(x + 1)}^{3}} = - \infty$

L.H.S:

$\begin{array}{rcl} \lim_{x \to - 1^{-}} \frac{5}{{(x + 1)}^{3}} & = & \lim_{h \to 0} \frac{5}{{(- 1 - h + 1)}^{3}} \\ = & \lim_{h \to 0} \frac{5}{{(- h)}^{3}} \\ = & \lim_{h \to 0} \frac{5}{- h^{3}} \\ = & \lim_{h \to 0} \frac{- 5}{h^{3}} \\ = & \frac{- 5}{0^{3}} \\ = & \frac{- 5}{0} \\ = & - \infty \end{array}$

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