Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use your knowledge of the derivative to compute the limit given.$$\lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h}$$

$$\frac{1}{2 \sqrt{x}}$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 2

Derivatives Rules 1

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Boston College

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:11

Use your knowledge of the …

01:05

Find each limit.$$…

01:28

07:14

Find the indicated limit.<…

01:26

Find the derivative of the…

01:22

Match the given limit with…

02:56

Evaluate $\lim _{h \righta…

01:04

Use the indicated new vari…

00:28

$$\lim _{h \rightarrow…

03:21

01:16

Find the limit by interpre…

02:43

Find the derivative of f(x…

13:50

Find limits

eso. What we have in front of us is the limit definition of the derivatives on. If you don't believe me, notice that it's a limit. H approaches zero of F of X plus h minus ffx all over h. So this is equal to the derivative of F as long as we can identify what f of X is equal to, um, if you heard me, I said it's f of X plus h minus ffx. So it makes perfect sense that FX has to be the square root of X. Now, as far as being able to do this problem, find the derivative makes more sense to rewrite that X to the one half power because we've learned the shortcut for the derivative, and that's moving that exploded in front. So it's one half X and you subtract one from that exponents, so it becomes negative one half power. You know, they have a needs help with one half minus one. So one half minus two halves would be negative one half. Now I would love my students to leave their answer like that. I know other teachers might prefer seeing an answer, you know, rewritten with a negative in the denominator and one half hours of square root, you know. So depending on your teacher, you might need to write it this way.

View More Answers From This Book

Find Another Textbook

05:05

Classify all critical points.$h(x)=4 x^{3}-13 x^{2}+12 x+9$

02:01

Find $d v / d t$ if $v=t^{2} \cdot \sqrt[3]{(2 t+8)^{2}}$.

02:29

Find $d y / d x$ if $y=\sqrt{\frac{x+1}{x-1}}$.

01:09

Suppose the cost of producing $x$ items is given by the equation $C(x)=x^{2}…

03:46

(a) Determine the extrema of the function defined by the equation $f(x)=\fra…

00:41

The position of an object at any time is given by the equation $s(t)=3 t^{3}…

Suppose postal requirements are that the maximum of the length plus girth (c…

06:03

A point moves along the circle $x^{2}+y^{2}=5$ in such a way that the distan…

01:33

Find $d y / d x$ using any method.$$x^{3}+y^{3}=10$$

02:10

Find $f^{\prime}(x)$ if $f(x)=\sqrt{2 x^{3}+3 x+2}$.