My Math Forum I can't show why x->0 of sin(x)/x is 1!!!

 Calculus Calculus Math Forum

 July 9th, 2019, 05:12 PM #21 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 triangle area = base × height / 2 = height / 2 if the base has length 1.
July 9th, 2019, 05:12 PM   #22
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Quote:
 Originally Posted by EvanJ I understand that, but what I don't know is how the left term of the inequality produced (sin x)/2 and how the right term produced (tan x)/2. Angle AEB is right, but isn't in those triangles. area of triangle ABD < area of sector ABD < area of triangle AFD
triangle ABD ... base = 1, height = sin x

triangle AFD ... base = 1, height = tan x

A = (1/2)bh

Last edited by skipjack; July 12th, 2019 at 04:19 AM.

 July 11th, 2019, 04:20 PM #23 Newbie   Joined: Jul 2019 From: Jordan Posts: 8 Thanks: 0 You can check it by using Taylor series. It will give you the answer in an easy way. Last edited by skipjack; July 12th, 2019 at 04:19 AM.

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