Limit of f(x) as x approaches infinity and solving for x=1: Homework Help

[Nope]

Homework Statement

http://img23.imageshack.us/img23/9366/95631341.jpg

http://img341.imageshack.us/img341/3416/37907619.jpg
lim f(x)
x->$$1\infty$$
I don't know how to do the first one..
ty!

Homework Equations

The Attempt at a Solution

 

[Mark44]

For the first problem, a through d and g are right, but e and f are wrong. The limit as x --> -1 is 1, not 3. Since both the left-side and right-side limits exist and are equal, the limit itself exists. It just happens that f(-1) is not equal to 1. That says that f is not continuous at x = -1.

 

[Nope]

I think i got it
just 1 more question,
lim (1.01+(1/n))ⁿ
x->$$\infty$$
How would you solve it?

 

[Mark44]

I think you mean as n --> infinity.
As n gets larger, 1.01 + 1/n approaches 1.01. When the quantity 1.01 + 1/n is raised to the power n, what happens to the whole expression?

Note that a similar limit, (1 + 1/n)^n has a quite different, and somewhat surprising limit value.

 

[Nope]

Is it infinity?
but when i put it in wolfram
the left side limit is 0? I don't get it... Does it mean, the limit does not exist?

 

[Mark44]

Yes (1.01 + 1/n)ⁿ approaches $\infty$ as n approaches $\infty$. I don't know what you're saying in regard to the left side limit -- n can approach $\infty$ only from one side. What are you asking?