Proving Limit Laws Using Delta Epsilon I need to prove that
$$\lim_{x\to a} f(x) = \lim_{h\to 0}f(a+h) $$ 
How would I start This! I need some willing to discuss this to a beginner who is lost Hints and detailed explanations wanted plssss
ALSO IS Subsitution given or does it have to be stated

Let us write $y=a+h$. Then, $\lim_{h\to0}f(a+h)=\lim_{y-a\to0}f(y)=\lim_{y\to a}f(y)$. This is the same as $\lim_{x\to a}f(x)$, but with a change of variable.
You could also do it this way: Using a Taylor expansion gives
$$f(a+h)=\sum^\infty_{k=0}\frac{f^{(k)}(a)}{k!}h^k=f(a)+\sum^\infty_{k=1}\frac{f^{(k)}(a)}{k!}h^k$$
As $h\to0$, $\sum^\infty_{k=1}\frac{f^{(k)}(a)}{k!}h^k\to0$. Therefore, $\lim_{h\to0}f(a+h)=f(a)$. Since $f(x)$ at $x=a$ is $f(a)$, $\lim_{x\to a}f(x)=\lim_{h\to0}f(a+h)$.
