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A cube is measured and each side is found to be 4 inches with a possible error of at most 0.005 in. Determine the approximate error in computing the volume of the cube.

At most 0.24 in $^{3}$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 6

Linearization and Differentials

Derivatives

Harvey Mudd College

Baylor University

University of Nottingham

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.

01:45

'point)The side o…

01:27

The length of each edge of…

01:07

The measurement of the edg…

01:08

The side of a cube is meas…

02:51

this question. We are told that a cube his site with maximum possible error. So there are 4" long and the maximum possible area of 0.03.05 inches. And we know that the volume of a cube is calculated by decides cubed all the side by side by side which is length with by height. And so to find the change the era we have to find tv T X which is the relationship between the volume and in the in the side. Now this is We do to differentiate the power comes down three X 10 -1. Get too. So we have this and we also know that the ratio of the error in volume over the ratio of the era in era is also equal to the the change in the movie. Over the change in X is equal to this uh ratio as well. So therefore we know that we can calculate our easy over er from this relationship. Therefore our E V will be equal to three X squared more play by are which is the era in in there. This is E x e X the era in the side. Yeah. Now putting in our four inches. Get three by four squared By 0.05. There are area in volume will be 0.24 inches cubed. And this is our solution. Yeah

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