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
Evaluate the limit, if it exists.
$ \displaystyle \lim_{t \to 1}\frac{t^4 - 1}{t^3 - 1} $
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
03:42
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 3
Calculating Limits Using the Limit Laws
Limits
Derivatives
Missouri State University
University of Nottingham
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
Evaluate the limit, if it …
01:01
Evaluate the limit.$$<…
00:49
Find the limit if it exist…
02:25
03:12
01:53
Evaluate the limit if it e…
00:40
Evaluate the limit:lim…
To evaluate this limit, we first rewrite teacher the 4th power -1. Overtake U -1. Since direct substitution gives us 1 to the 4th power -1 Over one K -1 which is just 0/0. An indeterminate value notes that T to the 4th power -1 over Take U -1. This is equal to t squared minus one times t squared plus one over T -1 times T squared plus t plus one. Which is the same as T -1 times t plus one times T squared plus one over t minus one times T squared plus t plus one. Now in here we can cancel out the T -1 and reduce the expression into T plus one times T squared plus one over T squared plus t plus one. And so using this we have this limit equal to limit as T approaches one of t plus one times t squared plus one over t squared plus t plus one which is just one plus one times one squared plus one over one squared plus one plus one, which is just 4/3. And so this is the value of the limit.
View More Answers From This Book
Find Another Textbook
02:10
A fruit merchant earns a profit of rs. 6 per bag oranges sold and a loss of …
01:09
By what rational number should 22/7 be Divided to get the number 11/24
02:22
10. Find the number which is: 53172 more than 64278 53172 less than 6427…
01:24
find three thousand one hundred thirty two added to thirty thousand and the …
02:34
write a quadratic polynomial whose zeros are 3-root2 and product of zeroes i…
08:24
An aircraft flies 400 km from a point O on a bearing of 025° and then 700 km…
01:46
a milkman has containers having capacity having capacity of 180 litres and 1…
03:24
Did you mean: if p and q are positive integers such as p>q prove that p2-…
01:45
a man sold his car for rupees 50000 loosing one tenth of its cost price find…
02:46
A house wife along with a group of ladies sold bags of different sizes. She …