SUNY Geneseo Department of Mathematics
Math 221 02
Fall 2020
Prof. Doug Baldwin
This discussion reinforces your understand of infinite limits, as described in “Infinite Limits” in section 2.2 of our textbook.
Please post at least one response to at least one of the following by class time on Wednesday, September 16.
Use the “Infinite Limits from Positive Integers” rule from the textbook, which really constitutes a limit law for infinite limits, to find the following limits. Say which of the 3 forms of the law you used where, and what the value of a is.
\[\lim_{x \to 0^-} \frac{1}{x^2}, \quad\lim_{x \to 0^+} \frac{1}{x^2}, \quad\lim_{x \to 0} \frac{1}{x^2}\] \[\lim_{x \to 0^-}\frac{1}{x^3}, \quad\lim_{x \to 0^+}\frac{1}{x^3}, \quad\lim_{x \to 0}\frac{1}{x^3}\] \[\lim_{t \to 1^-}\frac{1}{(t-1)^4}, \quad\lim_{t \to 1^+}\frac{1}{(t-1)^4}, \quad\lim_{t \to 1}\frac{1}{(t-1)^4}\]See if you can find, or can suggest ideas relevant to finding, these limits. You will probably need to use some ideas that weren’t discussed in the reading:
\[\lim_{x \to 1} \frac{x}{(x-1)^2(x+2)}\] \[\lim_{x \to -2^-} \frac{x}{(x-1)^2(x+2)}\] \[\lim_{x \to -2^+} \frac{x}{(x-1)^2(x+2)}\]