(a) Given that lim x0 (3x 1)(3x 1)x 2 0 01 0 01 prove that there exists an open interval (a, b) containing 0 such that (3x 1)(3x 1)x 2 0 01 0 for all x 0 in (a, b) (b) Given that lim xc g(x) L, where L 0, prove that there exists an open interval (a, b) containing c such that g(x) 0 for all x c in (...

a Since lim x0 3x 13x 1x2 001 001 we know that there exists a 0 such that if 0 x then 3 ...

(a) Given that lim x0 (3x + 1)(3x 1)x 2 + 0.01 = 0.01 prove that...

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(a) Given that

lim _x→0 (3x + 1)(3x − 1)x² + 0.01 = 0.01

prove that there exists an open interval (a, b) containing 0 such that (3x + 1)(3x − 1)x² + 0.01 > 0 for all x ≠ 0 in (a, b).

(b) Given that lim _x→c g(x) = L, where L > 0, prove that there exists an open interval (a, b) containing c such that g(x) > 0 for all x ≠ c in (a, b).

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Calculus Of A Single Variable

ISBN: 9781337275361

11th Edition

Authors: Ron Larson, Bruce H. Edwards

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(a) Given that lim x0 (3x + 1)(3x 1)x 2 + 0.01 = 0.01 prove that...

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a Since lim x0 3x 13x 1x2 001 001 we know that there exists a 0 such that if 0 x then 3...View the full answer

Calculus Of A Single Variable

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