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Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 2 1 lim I-2 2r 1 a. By l'Hôpital's Rule, lim -2 х —1 4 b. lim x sinx = lim f(x)g(x) ( lim 1)(lim cos x) = 1. c. lim x'* is an indeterminate form. d. The number 1 raised to any fixed power is 1. Therefore, be- cause (1 + x) → 1 as x→0, (1 + x) → 1 as x→0. e. The functions In x100 and In x have comparable growth rates as = lim f"(x) lim g'(x) = 0 f. The function e grows faster than 2ª as x→ .

Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 2 1 lim I-2 2r 1 a. By l'Hôpital's Rule, lim -2 х —1 4 b. lim x sinx = lim f(x)g(x) ( lim 1)(lim cos x) = 1. c. lim x'* is an indeterminate form. d. The number 1 raised to any fixed power is 1. Therefore, be- cause (1 + x) → 1 as x→0, (1 + x) → 1 as x→0. e. The functions In x100 and In x have comparable growth rates as = lim f"(x) lim g'(x) = 0 f. The function e grows faster than 2ª as x→ .

College Algebra
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
Section3.6: Rational Functions
Problem 2E
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Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 2 1 lim I-2 2r 1 a. By l'Hôpital's Rule, lim -2 х —1 4 b. lim x sinx = lim f(x)g(x) ( lim 1)(lim cos x) = 1. c. lim x'* is an indeterminate form. d. The number 1 raised to any fixed power is 1. Therefore, be- cause (1 + x) → 1 as x→0, (1 + x) → 1 as x→0. e. The functions In x100 and In x have comparable growth rates as = lim f"(x) lim g'(x) = 0 f. The function e grows faster than 2ª as x→ .
Transcribed Image Text:Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 2 1 lim I-2 2r 1 a. By l'Hôpital's Rule, lim -2 х —1 4 b. lim x sinx = lim f(x)g(x) ( lim 1)(lim cos x) = 1. c. lim x'* is an indeterminate form. d. The number 1 raised to any fixed power is 1. Therefore, be- cause (1 + x) → 1 as x→0, (1 + x) → 1 as x→0. e. The functions In x100 and In x have comparable growth rates as = lim f"(x) lim g'(x) = 0 f. The function e grows faster than 2ª as x→ .
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