Never mind you did. I couldn't tell at first.
Here are some worked out examples
http://www.math.ucdavis.edu/~kouba/C...l#SOLUTION%202
Use the precise definition to prove the following limit. Given epsilon, find a suitable delta to prove
lim 5x^2-3x-2 = 34
x->-3
So I got
5x^2-3x-36
|x+3| * |5x-12|
-1 < x+3 < 1
-4 < x < -2
-20 < 5x < -10
-32 < 5x-12 < -22
How do I find delta if my delta is negative?
Need help with these two as well.
Tried multiplying the conjugate with this one but ran into a dead end.
lim (Sqrt(2+x^2) - Sqrt(2-x^2)) / x^2
x -> 0
lim (x^(2/3)-4) / (x^(1/3)-2)
x -> 8
Thanks for the help!
Never mind you did. I couldn't tell at first.
Here are some worked out examples
http://www.math.ucdavis.edu/~kouba/C...l#SOLUTION%202
First of all, , it equals .
However, .
So, to prove , you need to show that for all .
So solve for .
.
.
Now, since taking a limit requires us to close in on the point , we can define to be a small value, e.g. , since we are going to make it smaller anyway...
So by defining , we have
So we can say , provided .
So define , and the proof will follow.