Consider The Following Arguments Concerning lim...


From: US
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Consider the following arguments concerning lim sin Pi /x, x→0+ . First, as x > 0 approaches ,Pi / x increases without bound; since sin t oscillates forincreasing t, the limit does not exist. Second: taking x =1, 0.1, 0.01, and so on, we compute sin Pi = sin 10 Pi =sin 100 Pi = 0; therefore the limit equals 0, Whichargument sounds better to you? Explain. Explore the limit anddetermine which answer is correct.


Answer No.1


From: US
Posts: 36
Votes: 72
As x approaches 0, π/x increases without bound, but no matter what the number of π/x, the range of sintis [-1, 1]. as π/x increases without bound, sint oscillatesfaster. that is, the range of sint become smaller and approaches tozero.

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