Answered: Evaluate the limit. 1000x - 6x + ax lim…

Evaluate the limit. 1000x - 6x + ax lim x0 1000+17x6 + e8 Give your answer in exact form. If the limit does not exist, enter DNE. 6x + xx 1000x lim xo 1000 + 17x6 + e8 %3D

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.4: Applications Of Eigenvalues And Eigenvectors

Problem 10E: Find the limit if it exists of Anx1 as n approaches infinity, where A=[02120], and x1=[aa]

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Question

Evaluate the limit.
1000x – 6x° + ax
lim
x→0 1000 + 17x6 + e8
Give your answer in exact form. If the limit does not exist, enter DNE.
1000x – 6x° + Tx
lim
x→0 1000 + 17x6 + e³

Expert Solution

Step 1

$s o l u t i o n : - \lim_{x \to \infty} \frac{1000 x - 6 x^{6} + {πx}^{5}}{1000 + 17 x^{6} + e^{8}} = \lim_{x \to \infty} \frac{x^{6} (\frac{1000}{x^{5}} - 6 + \frac{π}{x})}{x^{6} (\frac{1000}{x^{6}} + 17 + \frac{e^{8}}{x^{6}})} = \lim_{x \to \infty} \frac{(\frac{1000}{x^{5}} - 6 + \frac{π}{x})}{(\frac{1000}{x^{6}} + 17 + \frac{e^{8}}{x^{6}})}$

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