# Homework Help: Calculus: Limits

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1. Jun 27, 2015

### Ris Valdez

1. The problem statement, all variables and given/known data
Given that
lim f(x) = -4 and lim g(x) = 6
(All limits x --> +infinity)

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

2. Relevant equations

3. 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?

2. Jun 28, 2015

### Nathanael

Yep

3. Jun 28, 2015

### Ris Valdez

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

4. Jun 28, 2015

### PeroK

What else could the limit possibly be?

5. Jun 28, 2015

### Ris Valdez

Sorry! I was just making sure.

6. Jun 28, 2015

### 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.