lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.

# lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.

I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.

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