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 $ f $ is a quadratic function such that $ f(0) = 1 $ and$$ \int \frac{f(x)}{x^2 (x + 1)^3}\ dx $$is a rational function, find the value of $ f^\prime (0) $.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by J Hardin

Numerade Educator

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

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 4

Integration of Rational Functions by Partial Fractions

Integration Techniques

Harvey Mudd College

Baylor University

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

05:44

If $f$ is a quadratic func…

04:15

$f$ is a quadratic functio…

01:42

A rational function $f$ is…

01:37

01:09

State whether the function…

00:29

To find the ________ of a …

F is a quadratic function. F zero was one and were given that this in a girl's irrational function and would like to find at prime of zero. So let's come back up here and use this information. We have zero equal C equals one. So that gives us see So we have a of X equals x, where, plus b X plus one. And the thing that we're after is a primal zero. So that's just need. So we'd like to find the value of be such that this thing is rational function, so that will determine the possible values for me. So let's go ahead and do partial fraction to composition. So right now our instagram is f of X, which we know is that up there and then we have X squared. That's plus one cute. Now, using what the author calls case, too, I can write. This is ale rex be over ex players and then it using case to again, this time for X plus one she over X plus one deal Rex plus one square e over at plus one. Cute Oops And then let's go ahead and most supply Well, actually, at this case was before we multiply, we may not have to hear. Let's just note that we want this intervals to be irrational function. So, in particular, rational means we don't want logarithms No lots here, so that automatically eliminates these two terms here. We do not want these terms because these will give us natural logs. So this gives us a and sear both zero. So when I go ahead and multiply both sides by this denominator and we're getting rid of A and C score the next page, I get a X Square, be explicit one and then on the right, and then we could go ahead and solve this. So go ahead and expand the sow and then combine based on the power of ex supporter X cubed pullout of X squared. And that's what we're doing right now. So that's when you pull out X Square and then three b x. Well, then the and then we end up with three. B equals little bee. Large B is one, so that gives us B equals three. And that's exactly what we wanted. Because remember from the previous page, we wanted a crime of zero. We knew that was deep the be over here in front of the X, and we just found that value will be that gives us three, and that's your final answer.

View More Answers From This Book

Find Another Textbook

01:55

Question 8 01A bus covers a distance of 375 km at a certainspeed in …