Thread: Epsilon delta definition of limit.

Q1) The precise definition of lim x->a (f(x)≠L) is as follows

There exists an ε>0 such that for every δ>0 and if 0<|x-a|<δ then |f(x)-L|>ε

Show that lim x->0 sin(pi/x)≠L

note: Take L=0.19


Q2) Calculate lim x->1 (sqrt(x+8)) and prove it by using ε and δ definition of limit.

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about Q2 I find 0<|x-1|<δ and |sqrt(x+8)-3|<ε and |(sqrt(x+8)-3)*(sqrt(x+8)+3)/(sqrt(x+8)+3)|<ε equals |(x-1)/(sqrt(x+8)+3)|<ε Am I right


But about Q1 I can not find anything.

Q2: That's a good beginning, to write it more formal, we have to show that:

Proof:

Now, suppose therefore ... go further with this given to find for each a corresponding

Thank you. What about Q3?

Originally Posted by mervecetin

Q1) The precise definition of lim x->a (f(x)≠L) is as follows

There exists an ε>0 such that for every δ>0 and if 0<|x-a|<δ then |f(x)-L|>ε

Show that lim x->0 sin(pi/x)≠L

note: Take L=0.19

For Q1:

Start by inserting the given quantities, in this case L, a, and f(x), into the precise definition for the limit not existing.

Please, show us something.