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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 245

How could we visualize the proof (limx→0 sin(x)/x) ?

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,876

hi

Here's the proof that I was taught many years ago.

Draw a circle radius R and centre C. Mark points A and B as shown and D so that AD is perpendicular to CB.

Let angle ACB be x in radians.

sin(x) = AD / R

arc length AB / whole circumference = arcAB / 2.pi.R = angle of arc / whole circle angle = x / 2.pi

cancelling the 2.pi gives arcAB / R = x

So sin(x) / x = AD / arcAB

implies sin(x) < x but as x approaches zero AD approaches arcAB so sin(x) / x tends to 1.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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