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.
[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, .
What does "g(x)= x^2" have to do with this? There is no "g" in what you give.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 you mean then you need to know that . So this is the same as
No, the answer is NOT a number, it will be a function of a.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.
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!