Evaluate limit as x approaches infinity of e^(-2x)cos(x)

Math
Take the limit of each term.
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Split the limit using the Product of Limits Rule on the limit as approaches .
Since the exponent approaches , the quantity approaches .
Move the limit inside the trig function because cosine is continuous.
The limit at infinity of a polynomial whose leading coefficient is positive is infinity.
Multiply by .
Evaluate limit as x approaches infinity of e^(-2x)cos(x)

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