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

If $f^{\prime}(x)=2 e^{x},$ sketch the family of solutions.

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Campbell University

University of Nottingham

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

01:05

If $f^{\prime}(x)=\frac{-2…

04:34

Obtain a family of solutio…

04:05

If f prime of X is equal to two E. To the X sketch the solution family, acronym X equals two E. To the X is a differential equation for which we need to solve for Activex. Since F prime of X is purely a function of X, it involves other variables. We can take advantage of integration or specifically the anti derivative in order to solve this problem. So to obtain affects with anti deride F prime of X. Thus from anti derivation we obtain F of X equals two E. To the X plus C. Note that um gets its own anti derivative and we obtain see from the cost of integration. Thus, we want to sketch the solution family for different values of C. First we'll sketch for C equals zero. So alphabets equals two E to the X. Looks like this is simply an exponential function with double sample tube. Next we can sketch to E. X policy for different values of C. So firstly equals one. The graph rises for C equals negative four. We see that the graph of two E X policy moves vertically downward.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:48

Find and classify, using the second partial derivative test, the critical po…

03:15

Evaluate the given integral.$$\int x^{n} \ln (x) d x$$

01:02

Solve the given differential equation.$$\frac{d y}{d x}=3 x^{4} y^{4}$$<…

04:42

Evaluate the given integral.$$\int_{0}^{1} \int_{0}^{2}\left(x^{2}+y^{2}…

01:30

Use the method of Lagrange multipliers to optimize $f$ as indicated, subject…

01:01

Find $f(x)$.$$f^{\prime}(x)=3 e^{x}-\frac{2}{x^{2}}+1, f(2)=7$$

01:44

Evaluate the given integral.$$\int \frac{3 x+2}{3 x^{2}+4 x+1} d x$$

Find $f(x)$.$$f^{\prime \prime}(x)=x-2, f^{\prime}(2)=1, f(1)=-1$$

03:34

00:50

$f(x, y)=x / y,$ determine (a) $f(3,2),(\text { b) } f(2,3),(\text { c) } f(…