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The radius of a circular disk is given as $ 24 cm $ with a maximum error in measurement of $ 0.2 cm. $(a) Use differentials to estimate the maximum error in the calculated area of the disk.(b) What is the relative error? What is the percentage error?
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Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 10
Linear Approximation and Differentials
Derivatives
Differentiation
Campbell University
Oregon State University
Baylor University
Idaho State University
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.
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.
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The radius of a circular d…
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The radius $r$ of a circle…
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Okay. The driven of six X squared is 12 ax. Therefore, we know the maximum error 12 times, 30 times 0.1 gives us 36 centimeters squared. Therefore, relative errors. The area over the surface area therefore 36 divided by six times 30 squared gives 0.0 6/7 on then this ring as a percentage times 100 would be 0.67% for part B. We know that if us his pyre square that s prime of our In other words, the derivative would be two pi r. Therefore, we have to pie times 24 times changing our gives 9.6 pie centimeters squared.
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