Answered: (a) Find the limit. (If an answer does…

Math

Calculus

(a) Find the limit. (If an answer does not exist, enter DNE.) lim x→1 (x2 + x − 2)/(x2 − 1)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 63E

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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

(a)

Find the limit. (If an answer does not exist, enter DNE.)

lim x→1 (x² + x − 2)/(x² − 1)

(b)

Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)

lim x→−3 Sq.Root 46 − x-7/x+3

x	−3.1	−3.01	−3.001	−2.999	−2.99	−2.9
f(x)

lim x→−3 Sq.Root 46 − x-7/x+3 ≈

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$\lim_{x \to 1} \frac{x^{2} + x - 2}{x^{2} - 1}$

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