Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Evaluate the limit, if it exists.

$ \displaystyle \lim_{x \to 16}\frac{4 - \sqrt{x}}{16x - x^2} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{1}{128}$

02:42

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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 …

01:54

01:55

Evaluate the limit if it e…

01:08

Find the limit, if it exis…

01:32

Find the limit.$$\…

00:51

00:22

Find the limit.$\lim _…

to evaluate this limit. The first to direct substitution. That means We replace X x 16. And from here we get 4- the square root of 16 over 16 times 16 -16 16 square. That's equal to four minus four over 16 Squared -16 Squared. This gives us a value of 0/0 which is indeterminate. So we need to rewrite our function for minus squared of x over 16 X -X Squared. To do that. We will multiply the numerator and denominator by the conjugate of the numerator. That means we have four minus squared of X over 16 X minus x squared multiply this by four plus squared of x over four plus squared of X. And from here we have four squared minus the square of the squared of x over. We have 16 x minus x squared times four plus the square root of X. Now simplifying this, we have 16 minus x over can factor out X from here and we have X Times 16 -1 Times four Plus The Square Root of X. And in here we can cancel out the 16 -X. And we are left with one over X times four plus square the vex know that this function that call it G of X. And this function that's called it F of X. They both agree except for the value of X which is equal to 16. And so we can use this to find the limit of the original function F of X. That means we have The limit as X approaches 16. Four minus square defects over 16 X -X Squared. This is equal to The limit as x approaches 16 of one over x times four plus square Activex, and then evaluating at x equals 16. We have 1/16 Times four plus the squares of 16. That's equal to 1/16 times four plus four, and this will give us a value, which is equal to 1/1 28. And so this is the value of the limits.

View More Answers From This Book

Find Another Textbook