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Problem 2 Easy Difficulty

Given that
$$ \displaystyle \lim_{x\to a} f(x) = 0 $$ $$ \displaystyle \lim_{x\to a} g(x) = 0 $$ $$ \displaystyle \lim_{x\to a} h(x) = 1 $$
$$ \displaystyle \lim_{x\to a} p(x) = \infty $$ $$ \displaystyle \lim_{x\to a} q(x) = \infty $$
which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible

(a) $$ \displaystyle \lim_{x\to a} [f(x) p(x)] $$
(b) $$ \displaystyle \lim_{x\to a} [h(x) p(x)] $$
(c) $$ \displaystyle \lim_{x\to a} [p(x) q(x)] $$

Answer

a) indeterminate
b) $\lim _{x \rightarrow a} h(x) p(x)=\infty$
c) $\lim _{x \rightarrow a} p(x) q(x)=\infty$

Discussion

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Lyal E.

May 13, 2019

Video Transcript

So we're trying to determine which is an indeterminate form and which is uh much case does limit exists. So f of X times p of X is going to give us zero times infinity. And while you might think that zero, it's actually considered one of the indeterminate forms. Uh the fact that it says undefined doesn't matter too much because we'll see that that's often the case. Uh Once you get infinity involved, a lot of times things are undefined, but in this case it would be an indeterminate form. Then, for the second case we would get one times infinity, which is actually while it's not defined because infinity isn't defined, the limit would exist and it would be infinity. And then the last option is gonna give us infinity times infinity. Um And that would just be infinity. So in the three cases we just have one indeterminant form and that's going to be zero times infinity. Um And those are the cases in which will use the hotel's rule

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