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

If $ \displaystyle \lim_{x \to 1}\frac{f(x) - 8}{x - 1} = 10 $, find $ \displaystyle \lim_{x \to 1}f(x) $.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Campbell University

Baylor University

Idaho State University

Boston College

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.

04:02

If $$\lim _{x \rightarrow …

00:43

If $\lim _{x \rightarrow 1…

00:54

If $\lim _{x \rightarrow 2…

01:27

Find $\lim _{x \rightarrow…

This is problem number 59 of this to calculus edition section 2.3. If the limit as x, approaches 1 of the function f of x minus 8 over x, minus 1 is equal to 10 point find the limit as x approaches 1 of the function f. So, since we're given this definitive statement that this limit is equal to 10, we'll use our limit laws to rewrite this limit. Instead, as the limit as x, approaches 1 have f minus the limit is f x, approaches 1 of a divided by the limit as x, riches 1 of the quantity x minus 1 equals to 10 point. So we've used the laws that allow us to separate this quotient within the limit into the division of 2 limits and then the difference of limits in the top and the difference in set of a limit to the difference of limits at the top and notice that This term here is the term we want to solve, for so, let's go ahead, and do that multiply both sides limit is x, plus 1 of f minus limit is x, plus is 1 of 8 is equal to 10 times. This limit as x, approaches 1 of x minus 1. We can move the other limit to the right hand side. So, on the left hand, side we have limit as x, which is 1 of f equals 10 times the limit and which is 1 of the quantity x. Minus 1 plus e limit as x approaches 1 of 8. Now, as x, proches 1, this quantity x, minus 1, is equal to 1 minus 1 or 0 and 10 times 0 is 0. So what we end up getting is that the limit, as x, pushes 1 of f is equal to 0, plus this limit the limit of just 188 being in a constant value, therefore telling what is equal to 8- and this is our final answer as to what The limit is toast, 1 of f is.

View More Answers From This Book

Find Another Textbook

02:49

Students high schoo cijss exam On satet procequres below the mean? (Use the …

06:33

(12 points) The volume of the solid obtained by rotating the region enclosed…

03:23

For Problems 57-60, find (A) f' (x) (B) The slope of the graph of f at …

04:26

Consider the following4x8 + y7Find Y by implicit differentiation:

04:24

Mectom projectlon ofiv ontoIPdl F77pretwmUHRecompose Into two ve…

02:56

The current population of a town is 36000 and decreases at a constant rate o…

03:56

For your study O the food consumption habits of tecnage males, Jou randomly …

02:06

Find the indicated probability using the standard normal distribution P(z &l…

02:42

Whooping cough vaccine: Some parents fear that vaccinations may have adverse…