Evaluate the limit using the appropriate properties of limits. 8x - 9 lim x 9x2 + x - 3 Step 1 We are given the following. 8x2 - 9 lim x- 9x? + x - 3 We note that as x becomes large, both the numerator and the denominator become large. Therefore, it is not immediately obvious what happens to their ratio. So, we need to do some preliminary algebra. Recall that to evaluate the limit of a rational function at infinity, we first divide both the numerator and the denominator by the highest power of x that occurs in the denominator. Therefore, we should divide the numerator and the denominator by which of the following? Step 2 Since x? is the highest power of x in the denominator, we have determined that we will divide both the numerator and the denominator by x². Doing so and simplifying the result gives the following. (8x2 - 9) 8x2 - 9 lim lim x-- 9x? + x - 3 x- (9x2 + x - 3) (- -3) lim X

Evaluate the limit using the appropriate properties of limits. 8x - 9 lim x 9x2 + x - 3 Step 1 We are given the following. 8x2 - 9 lim x- 9x? + x - 3 We note that as x becomes large, both the numerator and the denominator become large. Therefore, it is not immediately obvious what happens to their ratio. So, we need to do some preliminary algebra. Recall that to evaluate the limit of a rational function at infinity, we first divide both the numerator and the denominator by the highest power of x that occurs in the denominator. Therefore, we should divide the numerator and the denominator by which of the following? Step 2 Since x? is the highest power of x in the denominator, we have determined that we will divide both the numerator and the denominator by x². Doing so and simplifying the result gives the following. (8x2 - 9) 8x2 - 9 lim lim x-- 9x? + x - 3 x- (9x2 + x - 3) (- -3) lim X

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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