(a) Estimate the value of ___________limx->-∞(√ x2 + x + 1 + x) by graphing the function . f(x) = limx->-∞(√ (x2 + x + 1 ) + x) (b) Use a table of values of f(x) to guess the value of thelimit.(c) Prove that your guess is correct.

(a) Estimate the value of ___________limx->-∞(√ x2 + x + 1 + x) by graphing the function . f(x) = limx->-∞(√ (x2 + x + 1 ) + x) (b) Use a table of values of f(x) to guess the value of thelimit.(c) Prove that your guess is correct.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5CC

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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) Estimate the value of

___________
lim_x->-∞(√ x² + x + 1 + x)

by graphing the function .

f(x) = lim_x->-∞(√ (x2 + x + 1 ) + x)

(b) Use a table of values of f(x) to guess the value of the
limit.
(c) Prove that your guess is correct.

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