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The edge of a cube was found to be $ 30 cm $ with a possible error in measurement of $ 0.1 cm. $ Use differentials to estimate the maximum possible error, relative, error, and percentage error in computing (a) the volume of the cube and (b) the surface area of the cube.

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(a) $270,0.01,1 \%$(b) $36,0.0067,0.6 \%$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Kate R.

February 24, 2022

Can you go over how you got to the answer for part b?

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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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:13

The edge of a cube was fou…

03:47

01:07

The measurement of the edg…

06:04

Volume and Surface Area Th…

The edge $x$ of a cube is …

We know that if we are vey Alexis X Cube than Devi over DX In other words, the derivative is gonna be three x squared. Therefore, we know three X squared times Delta acts is Delta V. Therefore we know relative errors error over the volume. So to 70 we got this by doing three times 30 squared times 0.1 over 30 cubed 0.1 0.1 The relative air times 100 gives us 1% is the maximum errors to 70 centimeters cubed relative a rose 0.1 and percentage error as a percent would be 1%.

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