Find the limits (that is, end behaviors) below. limx→−∞−5x(x−9)(x+6)6−8x3

Consider the given limit as limx→−∞−5x(x−9)(x+6)6−8x3 Compute the limit value as follows. limx→−∞−5x(x−9)(x+6)6−8x3=limx→−∞−5x3(1−9x)(1+6x)x3(6x3−8) =limx→−∞−5(1−9x)(1+6x)(6x3−8) =−5(1−0)(1+0)(0−8)=58 Thus, the given limit approaches 58 as x→−∞.

Expert answers to "Find the limits (that is, end behaviors) below...."

High School
Calculus and Analysis
Calculus 1
Limits and continuity

Maiclubk

Answered question

2021-10-12

Find the limits (that is, end behaviors) below.

lim_{x \to - \infty} \frac{- 5 x (x - 9) (x + 6)}{6 - 8 x^{3}}

Answer & Explanation

Jayden-James Duffy

Skilled2021-10-13Added 91 answers

Consider the given limit as

lim_{x \to - \infty} \frac{- 5 x (x - 9) (x + 6)}{6 - 8 x^{3}}

Compute the limit value as follows.

lim_{x \to - \infty} \frac{- 5 x (x - 9) (x + 6)}{6 - 8 x^{3}} = lim_{x \to - \infty} \frac{- 5 x^{3} (1 - \frac{9}{x}) (1 + \frac{6}{x})}{x^{3} (\frac{6}{x^{3}} - 8)}

= lim_{x \to - \infty} \frac{- 5 (1 - \frac{9}{x}) (1 + \frac{6}{x})}{(\frac{6}{x^{3}} - 8)}

= \frac{- 5 (1 - 0) (1 + 0)}{(0 - 8)} = \frac{5}{8}

Thus, the given limit approaches

\frac{5}{8}

x \to - \infty

Jeffrey Jordon

Expert2022-07-04Added 2605 answers

Answer is given below (on video)

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