Posted by **Liz** on Wednesday, June 27, 2012 at 1:07pm.

I have two similar problems that I need help completing. Please show all your work.

Question: Find the limit L. Then use the å-ä definition to prove the limit is L.

1. lim (2x+5)

x->3

2. lim 3

x->6

Thank you for your anticipated help!!

- Calculus -
**Liz**, Wednesday, June 27, 2012 at 1:08pm
**Note**

Please use the Epsilon-Delta Definition.

- Calculus -
**Count Iblis**, Wednesday, June 27, 2012 at 3:51pm
1)

f(x) = 2 x + 5

The limit for x to 3 is 11, assuming the function is continuous. To prove this, consider the open interval

I = (11-epsilon, 11+epsilon)

for some arbitrary epsilon

We want to find a delta > 0 such that the function f maps the open interval

J =(3-delta, 3+delta)

into I. That would then prove that for any arbitry epsilon>0 such a delta indeed exists. This means that no matter how small you take epsilon, there is always an interval containing x = 3 that will be mapped by f into the interval of size 2 epsilon containing 11.

If we solve:

2 x + 5 = y

for x, we get:

x = (y-5)/2

If we take y = 11 +/- epsilon, we get:

x = 3 +/- epsilon/2

So, we can take delta = epsilon/2

## Answer this Question

## Related Questions

- Calculus (lim) - consider the statement lim x³-6x²+11x-6 / x-1 = 2 x->1 Using...
- Calculus - How do I solve for lim h->0 (((a+h)^2 + 1)/(3(a+h)+7) - ((a^2 + 1...
- Math- Calculus - I need help with these problems, I cannot find a similar ...
- Calculus. Limits. Check my answers, please! :) - 4. lim (tanx)= x->pi/3 -(...
- calculus help please - hi what is lim as x reaches one of the function x/LN(x) ...
- calculus again - Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily ...
- Calculus - I don't know limits fairly well. The problem is prove the limit using...
- Calculus - HELP....last question SOS HELP Consider the statement lim X-->1 X...
- math - the limit of cuberoot((-3x^3+5x+2)/(x^2-1)) as x approaches 3 is the ...
- Check my CALCULUS work, please! :) - Question 1. lim h->0(sqrt 49+h-7)/h = ...

More Related Questions