Use properties of limits and algebraic methods to find the limit, if it exists.x2 - 81limX-9x + 9Step 1We want to use properties of limits and algebraic methods to findx2 - 81limx--9 x + 9Note that the function is a rationalfunction. The numerator and denominator are 0 atx = -9and thus we have the indeterminate form 0/0atX = -9We can factorfrom the numerator and reduce the fraction.x2 - 81x+9- 9)limX-9limX-9x + 9x + 9limX-9(x+9)(x – 9)(x + 9)-9-18

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Math

Calculus

Use properties of limits and algebraic methods to find the limit, if it exists. x² - 81 lim x--9 x + 9

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 110E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Use properties of limits and algebraic methods to find the limit, if it exists.
x2 - 81
lim
X-9
x + 9
Step 1
We want to use properties of limits and algebraic methods to find
x2 - 81
lim
x--9 x + 9
Note that the function is a rational
function. The numerator and denominator are 0 at
x = -9
and thus we have the indeterminate form 0/0
at
X = -9
We can factor
from the numerator and reduce the fraction.
x2 - 81
x+9
- 9)
lim
X-9
lim
X-9
x + 9
x + 9
lim
X-9
(x+9)(x – 9)
(x + 9)
-9
-18

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