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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 $

(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.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Campbell University

Harvey Mudd College

Baylor University

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This is problem number three of Stuart eighth edition, Section two point two. Explain the meaning of each of the following. First we start with party the limit as X approaches Negative three of equals. Infinity. So what this means is that as the function of earth approaches negative three, that the closer it gets the negative three the closer that he gets to infinity Infinity here, representing a very, very, very, very large number. And so the function atthe well, never touch this imaginary line at negative three. So it is not to find a native three necessarily. But it approaches a very, very large infinite number as it gets closer to negative three. Because Islam, it does not have a superscript of a negative or positive. Then this limit here in party is a limited from the left and the right, um, completely. So that means that the function from both the left and the right approach infinity or a very large number as Africa's closer to negative three for part being, we look at to limit as ex purchase for specifically from the right and we see that the function approaches and negative infinity as this happens So you have a function f and I think because it's closer to four from the right, as in from numbers larger than for the closer it gets to four. From the right closer, he gets to negative unity or a very large negative number and the graft to the right. Displace this exactly, and this is all that is needed to confirm that limit. And now we can see the difference between a statement, a statement be.

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