Determine lim x->(infinity) 2^x +sin(x)

Question

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

Answer 1

Thanks for clearing that up.

 

Let's look at this in pieces.  

 

1) Lim as x--> infinity of 2^x = infinity

 

2) 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.