Wednesday, 12 November 2014

How can I find limits without L'Hopital's Rule?





My question is, how can I evaluate limits without L'Hopital's Rule ?



limx0sin(3x)1cosx


Answer



For small x, 1cosx=2sin2x2x22 while sin3x3x, so sin3x1cosx2x5/3 diverges as x0. Thus the limit is .


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