# Thread: need help on delta epsilon proof

1. ## need help on delta epsilon proof

if is a polynomial, then

so i have |x-a|< δ
and |p(x)-p(a)|< ε

2. Some rules:

If $\lim_{x \to a} f(x) = L$ and $\lim_{x \to a} g(x) = M$

then $\lim_{x \to a} (f+g)(x)=L+M$ and $\lim_{x \to a} (fg)(x)=LM$

also $\lim_{x \to a} \ (kf)(x) = kL$

Prove that $\lim_{x \to a}x = a$

Now use the product rule and induction to show that $\lim_{x \to a}x^{n} = a^{n}$

Finally use the mutiple rule and the sum rule