Calculate \( \lim_{ x \to 2} f(x) \)
and \( \lim_{ x \to 0} f(x) \)
for each of the following.
- \( f(x) = (x^{3}-x-6)/(x-2) \)
- \( f(x) = (x^{4}-x^{2}-6x)(x^{2}-2x) \)
- \( f(x) = [(2+x)^{\pi}-2^{\pi}]/x \)
- \( f(x)=
\begin{cases}
(\sqrt{x^{2}+6x} - 4)/(x-2), & \text{when } x>2 \\
5|x|/(4x) & \text{when } x\leq 2
\end{cases} \)
Tags: limits, rational, higher-polynomial, root, absolute-value, piecewise-defined, computation, rote-problem, a--a, t2, c2
Parts c and d require the definition of derivative.
ADD KEYWORDS: "using a definition" AND "differentiation" AND "piecewise-defined"– Concha Gomez 1999-02-19