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Problem 28 Easy Difficulty
Prove that the series obtained in Exercise 25 represents $ \sin x $ for all $ x. $
Answer
show that the remainder $\rightarrow 0$ with Taylor's inequality, so the sum of the
series is equal to the function by "Theorem 8"
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Video Transcript
The problem is proof that if Siri's of finding exercise on Your staff represents sign acts for all acts, so first in exercise on the farm we have Siri's is some on from zero to infinity makes you want to the part of plus one times X minus pi two, two and one over two and plus one factorial so we can see this is on alternating Siri's. So they are donating Siri's estimation. Siri, um, show that error involved in this approximation. Our shoe and last one Thanks absolutely with this one is last X minus pi Absolute value shuen plus three over shuen plus three factorial the's the limit and goes to infinity Xmas pie to end Class three offer it to M plus three. Bacterial is equal to zero for honey Max, it's over half limit, uh, shoe and plus one. What endorsing twenties? Got zero max. Then we have the theories. Siri's represents sign axe for all Axe
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