- #1
zeion
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Homework Statement
Prove the follow statements directly using the formal [tex] \epsilon , \delta [/tex] definition.
[tex] \lim_{x\rightarrow 1} \frac{x + 3}{x^2 + x + 4} = \frac{2}{3} [/tex]
Homework Equations
The Attempt at a Solution
[tex] 0 < |x - 1| < \delta \rightarrow 0 < |\frac{x + 3}{x^2 + x + 4} - \frac{2}{3}| < \epsilon [/tex]
Not sure what to do now.
0 < | 3(x+3) - 2(x2 + x + 4) / 3(x2+x+4) | < e
0 < | -2x2 + x + 1 / 3(x2+x+4) | < e
0 < | (-2x - 1)(x - 1) / 3(x2+x+4) | < e
Now I can control (x - 1), but how do I do this?