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Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) allows for an alternate way of calculating the numerical value of a function. The series expansion for the sine function, with the angle in radians, is: Sometimes, mathematical functions are written as "series expansions." This 03 05 07 +. 31 51 71 The exclamation points are factorials. This equation is the basis for the small angle sin 0 0- + ** approximation, which says that when an angle is small (and in radian): sin 0 0 This approximation holds because when the angle is much less than 1, the subsequent terms become negligible due to the exponents. At what angle is the magnitude of the second term G.) in the series expansion equal to 2% of the magnitude of the first term ( 0)? (You can ignore the positive or negative signs; convert your final answer to degrees.)
Transcribed Image Text:(3) allows for an alternate way of calculating the numerical value of a function. The series expansion for the sine function, with the angle in radians, is: Sometimes, mathematical functions are written as "series expansions." This 03 05 07 +. 31 51 71 The exclamation points are factorials. This equation is the basis for the small angle sin 0 0- + ** approximation, which says that when an angle is small (and in radian): sin 0 0 This approximation holds because when the angle is much less than 1, the subsequent terms become negligible due to the exponents. At what angle is the magnitude of the second term G.) in the series expansion equal to 2% of the magnitude of the first term ( 0)? (You can ignore the positive or negative signs; convert your final answer to degrees.)
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