Kenneth S. answered • 03/12/17
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I do not see the need for -0 after tan x in the denominator. Nor do I see a need for l'Hôpital's rule.
If we replace denominator tan x by sin x / cos x then we are taking the limit (toward 0) of
[xcosx / sinx - cos2x] = lim cos x (x/sinx) - lim cos2x and that is 1(1) - 12 = 0.
Arturo O.
I should have written the comment as
limx→0 [x/sin(x)] = limx→0 [1/cos(x)] = 1/1 = 1
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03/12/17
Kenneth S.
Hi, Arturo. The limit x/sinx is usually proven via a geometric argument early in a Calculus class (which I'm sure you know).
The fact that it can also be shown to be 1 (as x approaches zero) also by using l'Hôpital's rule is valid, but said rule usually occurs a bit later in the course.
Anyway, I dislike instructions that dictate which method should be used. I prefer questions to be solved by whatever a student has in his or her repertoire at any given time. The real world gives us problem, usually without directions.
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03/12/17
Arturo O.
Kenneth,
Sometimes the teacher directs the student to use a particular method, just to prove the student knows how to use it. That may have been the case here.
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03/12/17
Arturo O.
03/12/17