Use Graph to Find Delta...1

[nycmathguy]

Calculus
Section 2.4

Can you work out 5 as a guide for me to do 6 on my own? Jenn does not teach how to do this in her video lessons.

 

[MathLover1]

5.
use the graph to find delta if |x-2|<δ then |sqrt(x^2+5)-3|<0.3

The function is y=sqrt(x^2+5)

find delta if |x-2|<δ whenever |sqrt(x^2+5)-3|<0.3

We need to establish a connection between |x-2|<δ and |sqrt(x^2+5)-3|<0.3

Consider |sqrt(x^2+5)-3|<0.3

Solve the inequality.

-0.3< |sqrt(x^2+5)-3|<0.3

-2.42693<x<-1.51327
or
1.51327<x<2.42693


Since δ>0

0< |x-2|<δ

0< |x-2|<2.42693

Compare the inequality above

δ=2.42693

 

[nycmathguy]

5.
use the graph to find delta if |x-2|<δ then |sqrt(x^2+5)-3|<0.3

The function is y=sqrt(x^2+5)

find delta if |x-2|<δ whenever |sqrt(x^2+5)-3|<0.3

We need to establish a connection between |x-2|<δ and |sqrt(x^2+5)-3|<0.3

Consider |sqrt(x^2+5)-3|<0.3

Solve the inequality.

-0.3< |sqrt(x^2+5)-3|<0.3

-2.42693<x<-1.51327
or
1.51327<x<2.42693


Since δ>0

0< |x-2|<δ

0< |x-2|<2.42693

Compare the inequality above

δ=2.42693

You learned this stuff long ago and still remember how to do it. Amazing.

 

[MathLover1]

You learned this stuff long ago and still remember how to do it. Amazing.

I learned that 47 years ago.

 

[nycmathguy]

I learned that 47 years ago.

I watched two samples of the epsilon-delta definition with Jenn today. I am still confused. Wow! How time flies!!! She struggled to break down the material. It was easy to see that for each problem. Mira, if I could cancel the membership, I would.

 

[nycmathguy]

I learned that 47 years ago.

Mira,

Here is your chance to contact Tom at the website:

Maybe you have some questions for him about Jenn and her website. I will now text my reply to Tom. Check your PM.