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

In summary, the limit of [f(x) + 2g(x)] as x approaches positive infinity is 8. This can be determined by using the basic properties of limits, which state that for any constant A and two existing limits, the limit of A*f(x) is A times the limit of f(x), and the limit of the sum of two functions is the sum of the limits of each individual function. Therefore, the limit can be found by substituting the given limits of f(x) and g(x) into the equation and simplifying.
  • #1
Ris Valdez
9
0

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?
 
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  • #2
Ris Valdez said:
Did I do it right?
Yep
 
  • #3
Nathanael said:
Yep
Thanks! It was a wiley assignment and I thought I did it wrong xD
 
  • #4
Ris Valdez said:
Thanks! It was a wiley assignment and I thought I did it wrong xD

What else could the limit possibly be?
 
  • #5
PeroK said:
What else could the limit possibly be?
Sorry! I was just making sure.
 
  • #6
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.
 

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

1. What is a limit in calculus?

A limit in calculus refers to the value that a function approaches as the input approaches a specific value. It is used to determine the behavior of a function at a particular point and is an essential concept in calculus.

2. How do you solve for a limit in calculus?

To solve for a limit in calculus, you need to use algebraic techniques, such as factoring, cancelling, and simplifying, to manipulate the given function until you can substitute the desired value for the input. Then, you can evaluate the function and determine the limit.

3. What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit refers to the value that a function approaches from either the left or the right side of a specific point. On the other hand, a two-sided limit refers to the value that a function approaches from both the left and the right side of a specific point.

4. How do you solve for a limit of a sum of two functions?

To solve for a limit of a sum of two functions, you can use the limit properties, which state that the limit of a sum of two functions is equal to the sum of their individual limits. Therefore, you can solve for each limit separately and then add them together to find the limit of the sum.

5. Can the limit of a sum be equal to the sum of the limits of individual functions?

Yes, the limit of a sum can be equal to the sum of the limits of individual functions. This is known as the limit addition property, which states that the limit of a sum is equal to the sum of the limits when both limits exist. However, this property does not apply to other operations, such as multiplication, division, or composition of functions.

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