Calculus: Limits - Solving for Lim[f(x) + 2g(x)]

[Ris Valdez]

Homework Statement

Given that
lim f(x) = -4 and lim g(x) = 6
(All limits x --> +infinity)

Find the limit
lim [f(x) + 2g(x)]

Homework Equations

The Attempt at a Solution

So I substituted the values of f(x) and g(x) in the equation

=[(-4) + 2(6)
the limit is = 8

Did I do it right?

 

[Nathanael]

Did I do it right?

Yep

 

[Ris Valdez]

Yep

Thanks! It was a wiley assignment and I thought I did it wrong xD

 

[PeroK]

Thanks! It was a wiley assignment and I thought I did it wrong xD

What else could the limit possibly be?

 

[Ris Valdez]

What else could the limit possibly be?

Sorry! I was just making sure.

 

[HallsofIvy]

You should know from basic properties of limits that
1) For any constant A, as long as lim f(x) exists, then so does lim Af(x) and the limit is A(lim f(x)).
2) As long as lim f(x) and lim g(x) exist, then so does lim f(x)+ g(x) and the limit is lim f(x)+ lim g(x).

Those two together give the result you want.