finding 2 limits. Unsure of answer.

I'm trying to find limits for 2 situations.

1. lim x->a

f(x)-f(a) if f(x)=x^2+4 gave me lim x ->a = 2a

--------

x-a

2. lim x->a

f(x)*(x^3-a^3) if f(x)=a^3 and g(x)=a^2 so I got lim x->a = 2a^2(a+1)

---------------

(x-a)*a^2

My main concern is that so far in every situation where we had a letter instead of a number we could get rid of the letters eventually and get a number.

I'm wondering if the answers are correct and if not what might be the correct answer and/or steps to get there.

Thank you.

Re: finding 2 limits. Unsure of answer.

Quote:

Originally Posted by

**Raitor**

1. lim x->a

f(x)-f(a) if f(x)=x^2+4 gave me lim x ->a = 2a

--------

x-a

What is f(a) if ?

To start you out:

The rest I leave up to you.

-Dan

Re: finding 2 limits. Unsure of answer.

[QUOTE=Raitor;735446]I'm trying to find limits for 2 situations.

1. lim x->a

f(x)-f(a) if f(x)=x^2+4 gave me lim x ->a = 2a

--------

x-a

Unfortunately, The internet does not always "respect" spaces. f(x)= (x^2+ 4)/(x- a). But since we cannot divide by 0, f(a) does not exist so f(x)- f(a) does not exist. Do you mean just "lim f(x) as x goes to a?. Well that also does not exist.

I **think** you mean "find where .

Okay, if that is true, .

Quote:

2. lim x->a

f(x)*(x^3-a^3) if f(x)=a^3 and g(x)=a^2 so I got lim x->a = 2a^2(a+1)

---------------

(x-a)*a^2

What does "g(x)= x^2" have to do with this? There is no "g" in what you give.

If you mean then you need to know that . So this is the same as

Quote:

My main concern is that so far in every situation where we had a letter instead of a number we could get rid of the letters eventually and get a number.

No, the answer is NOT a number, it will be a function of a.

Quote:

I'm wondering if the answers are correct and if not what might be the correct answer and/or steps to get there.

Thank you.

Re: finding 2 limits. Unsure of answer.

Quote:

Originally Posted by

**Raitor** 2. lim x->a

f(x)*(x^3-a^3) if f(x)=a^3 and g(x)=a^2 so I got lim x->a = 2a^2(a+1)

---------------

(x-a)*a^2

If then f(x) is a constant. Same for g(x). I think you need to re-state this.

-Dan

Re: finding 2 limits. Unsure of answer.

Thank you for your quick answers.

I'll rewrite the whole thing also taking into account what you told me and I made a couple mistakes while writing down the second problem.

1. Evaluate where

I ended up doing this :

= = = = =

2. For and evaluate the limit of :

For this I did the following.

= = = = = =

Wish I had known about this way to insert equations on the forums the first time around.

Would those answers be correct? What about the way I wrote the equations?

Thank you again!