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One side of a right triangle is known to be $ 20 cm $ long and the opposite angle is measured as $ 30^o, $ with a possible error of $ \pm 1^o. $(a) Use differentials to estimate the error in computing the length of the hypotenuse.(b) What is the percentage error?

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(a) estimated error: $\pm 1.209 \mathrm{cm}$(b) percentage error: $\pm 3 \%$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

04:05

One side of a right triang…

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46. One side of a right tr…

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The hypotenuse of a right …

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Okay, Part A. We know that D h. The differential is negative. 20 coast seeking acts Times CO changing Axe de Axe. Therefore, we have negative 20 caustic up, 30 degrees could tangent 30 degrees and then the possible error was remember it was plus or minus pi over 1 80 which simplifies to plus or minus 1.209 centimeters. Therefore, we have de age equals pulsar minus 1.209 centimeters, divided by 20 caustic it 30 degrees. That's 20 times two, which is 0.3 right. This is a percentage this is plus or minus 3%.

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