- #1
roadworx
- 21
- 0
Homework Statement
Use the precise definition to show
[tex]lim (x^2+3x) = 10[/tex]
x[tex]\rightarrow[/tex]2
The Attempt at a Solution
Let [tex]\epsilon[/tex] > 0
[tex]x^2 + 3x - 10 < \epsilon [/tex]
[tex](x-2)^2 = x^2 - 4x + 4 [/tex]
This doesn't equal the equation. Add 7x, -14
[tex]\left| x-2 \right| ^2 + 7 \left| x-2 \right| [/tex]
So far it's alright. Now I need to get a value for [tex]\delta[/tex]
[tex]\epsilon[/tex] = [tex]\delta^2 + 7 \delta[/tex]
Now I'm totally confused. Normally I've used simply [tex]\delta[/tex] expressions like [tex]\delta[/tex] = [tex]\epsilon[/tex]/2. What should I say my [tex]\delta[/tex] is equal to in this case, and why?
So [tex]\left| (x^2 + 3x) -10 \right|[/tex] < [tex]\delta^2 + 7 \delta[/tex]
Any help?