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Numerade Educator

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Problem 3 Easy Difficulty

Explain the meaning of each of the following.
(a) $ \displaystyle \lim_{x\to-3}f(x) = \infty $ (b) $ \displaystyle \lim_{x\to4^+}f(x) = - \infty $

Answer

(a) $\lim _{x \rightarrow-3} f(x)=\infty$ means that the values of $f(x)$ can be made arbitrarily large (as large as we please) by taking $x$
sufficiently close to -3 (but not equal to -3 ).
(b) $\lim _{x \rightarrow 4^{+}} f(x)=-\infty$ means that the values of $f(x)$ can be made arbitrarily large negative by taking $x$ sufficiently close to 4 through values larger than 4.

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Video Transcript

for this problem, we are to explain the meaning of each of the following. The first one is the limit of F of X. As X approaches negative three equals an infinite value, and the other one is that the limit of F of X as X approaches for from the right is a negative infinite value. Now the first one tells us that whenever access close to negative three but not equal to negative three, the value of F of X is a large positive number. And since the limit value is infinite as X gets closer and closer to negative three, we can say that the value of F of X gets bigger and bigger, or that it increases without bound. And with this description we see that this represents the vertical S M dot of the function at X equals negative three. For part B. This tells us that whenever X is close to four but not equal to four, and we are approaching for from the right, the value of F of X is a large negative number. And since the limit value is infinite, as X gets closer and closer to four from the right F of X gets smaller and smaller, or that it decreases without bound. This also tells us that the function has a vertical sm towed at X equals four.