We have an answer to "What is the limit as x→∞ of e−2xcos⁡x?"

mascaraspx2

Answered question

2023-01-20

What is the limit as

x \to \infty

e^{- 2 x} \cos x

Gary Montoya

Beginner2023-01-21Added 9 answers

We need remember that

- 1 \leq \cos x \leq 1 \Rightarrow - e^{- 2 x} \leq e^{- 2 x} \cdot \cos x \leq e^{- 2 x}

Then

lim_{x \to \infty} - e^{- 2 x} \leq lim_{x \to \infty} e^{- 2 x} \cos x \leq lim_{x \to \infty} e^{- 2 x}

But

lim_{x \to \infty} - e^{- 2 x} = lim_{x \to \infty} e^{- 2 x} = 0

Therefore

lim_{x \to \infty} e^{- 2 x} \cos x = 0

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