Problem 27

In Exercises 21-28, use the graph to find the lim…

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Problem 27

In Exercises 21-28, use the graph to find the limit (if it exists). If the limit does not exist, explain why.
$$\lim _{x \rightarrow 0} \cos \frac{1}{x}$$
Problem 28

In Exercises 21-28, use the graph to find the limit (if it exists). If the limit does not exist, explain why.
$$\lim _{x \rightarrow \pi / 2} \tan x$$
Problem 29

Graphical Reasoning In Exercises 29 and 30 ,use the graph of the function $f$ to decide whether the value of the given quantity exists. If it does, find it. If not, explain why.

(a) $f(1)$
(b) $\lim _{x \rightarrow 1} f(x)$
(c ) $f(4)$
(d) $\lim _{x \rightarrow 4} f(x)$
Problem 30

Graphical Reasoning In Exercises 29 and 30 ,use the graph of the function $f$ to decide whether the value of the given quantity exists. If it does, find it. If not, explain why

(a) $f(-2)$
(b) $\lim _{x \rightarrow-2} f(x)$
(c) $f(0)$
(d) $\lim _{x \rightarrow 0} f(x)$
(e) $f(2)$
(f) $\lim _{x \rightarrow 2} f(x)$
(g) $f(4)$
(h) $\lim _{x \rightarrow 4} f(x)$
Problem 31

In Exercises 31 and $32,$ sketch the graph of $f$ . Then identify the values of $c$ for which $$\lim _{x \rightarrow e} f(x)$$

$$f(x)=\left\{\begin{array}{ll}{x^{2},} & {x \leq 2} \\ {8-2 x,} & {2 < x < 4} \\ {4,} & {x \geq 4}\end{array}\right.$$
MM
Meghan M.
Problem 26

In Exercises 21-28, use the graph to find the limit (if it exists). If the limit does not exist, explain why.$$\lim _{x \rightarrow 5} \frac{2}{x-5}$$

Answer

Limit does not exist

Chapter 1
Limits and Their Properties
Section 2
Finding Limits Graphically and Numerically
Calculus of a Single Variable

Topics

Limits of a Function

Discussion

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Video Transcript

I can't. And this problem We want to find the limit as X approaches five for this function f of X. So if you look at the graph of the facts, we see that there's a vertical pass and toke at X equals five. She kind of unsure of how you know that this expertise five him kind of look, the scaling of the graph. So if this right here is six, this one here, my must be four and two. So right in the middle should be X equals five. So So from the left. So we see that the left hand limit as we approach X equals five, appears to be going down towards negative infinity. So that left him in a minute. It is negative infinity, because it kind of keeps going down and down infinitely. And now if we look ATT behavior from the right, we see that the right hand who limit as we approach X equals five. It is going in a complete opposite direction. It's approaching positive, Anthony. So that is positive. Infinity. So since the left and right limits, I don't agree, and they are both infinite values. The limit does not exist, So he say limit does not exist. If the left right limits don't I agree? That's one case. Another case is when one or both of the limits are infinite value. So in this case, the women doesn't exist for both of those who since, actually so the limit is expert, just five for this function does not exist.

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