Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
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 $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Ma. Theresa Alin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:20
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 2
The Limit of a Function
Limits
Derivatives
Campbell University
Oregon State University
Baylor University
Idaho State University
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
0:00
Explain the meaning of eac…
02:46
01:17
Explain in your own words …
02:38
01:07
$$ \begin{array}{l}{\text …
01:11
For the given $f(x),$ expr…
02:19
$$\text { Explain the mean…
03:51
Find each limit. Use $-\in…
02:10
Evaluate each limit. If th…
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.
View More Answers From This Book
Find Another Textbook
01:29
"forensic psychologist studying the accuracy of a new type of polygraph…
02:04
'A forensic psychologist studying the accuracy of a new type of polygra…
01:26
'7,3.7Rewrite the following expression in terms of exponentials and…
02:31
'Refer to the graph ofy = f(x) =x2 _ x shown: a) Find the slope of the …
01:02
'Problem Knowing that at the instant shown the angular velocity of rod …
02:06
'Write polynomial function of minimum degree with real coefficients who…
05:22
'Find the area of the part of the plane3y + 2 = 15 that lies in the…
02:11
'Tt Write the value of sin x2 dx as an infinite series. Hint: There is …
03:47
'It is believed that as many as 23% of adults over 50 never graduated f…
01:19
'An ice cream store sells 22 flavors of ice cream. Determine the number…
