Books(current) Courses (current) Earn 💰 Log in(current)

Problem 27

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

00:30
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 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86
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

You must be signed in to discuss.

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.

Recommended Questions