Mathalina S.

asked • 01/09/16# Determine lim x->(infinity) 2^x +sin(x)

How do I solve this? The sine is really confusing me

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## 1 Expert Answer

Marlene S. answered • 01/09/16

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Retired Actuary with 20+ years of Calculus Tutoring Experience

Thanks for clearing that up.

Let's look at this in pieces.

1) Lim as x--> infinity of 2

^{x}= infinity2) Lim as x--> infinity of sin(x) will approach -1, 0, or 1.

Think of the unit circle. The smallest sin(x) can be is -1 and the largest sin(x) can be is +1.

But this really doesn't matter as -1 or +1 will not have an effect when added to infinity.

Infinity + anything = infinity

So the limit is infinity.

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Marlene S.

01/09/16