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CalculusQ&A LibraryGiven that limx→0cos x = 1, which of the following statements is true?(a) If |cos x − 1| is very small, then x is close to 0.(b) There is an E > 0 such that if if 0 < |cos x − 1| < E, then |x| < 10−5 .(c) There is a δ > 0 such that if 0 < |x| < δ, then |cos x − 1| < 10−5.(d) There is a δ > 0 such that if 0 < |x − 1| < δ, then |cos x| < 10−5.Question

Asked Feb 14, 2020

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Given that lim

x→0

cos x = 1, which of the following statements is true?

(a) If |cos x − 1| is very small, then x is close to 0.

(b) There is an E > 0 such that if if 0 < |cos x − 1| < E, then |x| < 10−5 .

(c) There is a δ > 0 such that if 0 < |x| < δ, then |cos x − 1| < 10−5.

(d) There is a δ > 0 such that if 0 < |x − 1| < δ, then |cos x| < 10−5.

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