- #1

- 78

- 0

## Homework Statement

lim x ---> infinity (x/x+1)^99

(lim of x over (x+1) all raised to the 99th power)

## Homework Equations

## The Attempt at a Solution

The answer in my solutions manual is 1. I'm so lost. Any tips would be appreciated.

- Thread starter Sentience
- Start date

- #1

- 78

- 0

lim x ---> infinity (x/x+1)^99

(lim of x over (x+1) all raised to the 99th power)

The answer in my solutions manual is 1. I'm so lost. Any tips would be appreciated.

- #2

- 78

- 0

I know the limit of the inside is one if you use l'hopital but the 99 exponent is throwing me off

- #3

- 50

- 0

Divide the numerator and denominator by x. So at the numerator you now have 1. The denominator is now 1 + 1/x. When x goes to infinity 1/x will go to 0. So then you have (1/1)^99 = 1.

- #4

Mark44

Mentor

- 34,331

- 5,974

Use more parentheses!## Homework Statement

lim x ---> infinity (x/x+1)^99

What you have inside the parentheses would reasonably be interpreted exactly the same as (x/x) + 1. I doubt that's what the problem showed.

The expression you're taking the limit of should be written as (x/(x + 1))

Your textbook should have some examples where they take the log of the limit expression, and then take the limit.(lim of x over (x+1) all raised to the 99th power)

## Homework Equations

## The Attempt at a Solution

The answer in my solutions manual is 1. I'm so lost. Any tips would be appreciated.

- #5

- 78

- 0

Mark, first off sorry about the parentheses, i need to be specific

Second, i remember an example from class now. take the log, and move the 99 in front. From there, do you also use eliya's method of dividing everything by x? ( the (x/(x+1)) inside the log)

- #6

lurflurf

Homework Helper

- 2,432

- 132

Your book should have a lemma like

lim f(g(x))=f(lim g(x))

lim (g(x))^99=(lim g(x))^99

- #7

- 78

- 0

I had forgotten that too! Thank you very much

Your book should have a lemma like

lim f(g(x))=f(lim g(x))

lim (g(x))^99=(lim g(x))^99

- #8

- 78

- 0

If a function is continuous and I take a limit "inside" can l'hopital's rule be used inside as well?

- #9

Mark44

Mentor

- 34,331

- 5,974

If the expression you're taking the limit of is suitable for L'Hopital's Rule, yes.

- #10

Mark44

Mentor

- 34,331

- 5,974

That doesn't matter. If you have a limit expression that L'Hopital's can be used on, go for it. You've already switched the limit and ln operations.If a function is continuous and I take a limit "inside" can l'hopital's rule be used inside as well?

- #11

- 446

- 1

Divide top and bottom by [tex](\frac{1}{x})^{99}}[/tex] and take the limit ...

- Replies
- 6

- Views
- 673

- Replies
- 25

- Views
- 2K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 352

- Last Post

- Replies
- 16

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Replies
- 18

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 550