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Differential Calculus

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31 Dec 2009 15:57:44 IST

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evaluate..lim x tends to 0 [sinx/x] [ ] represents greatest integer function...

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evaluate..lim x tends to 0 [sinx/x] [ ] represents greatest integer function...

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kabi

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Joined: 11 Jan 2009

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31 Dec 2009 16:26:12 IST

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lim_x--->0 sin(x)/x is 1 .

But actually sin(x) <x

so the ratio would tend to 1 or we can say its GIF is 0

Thank u

Dharav Solanki

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1 Jan 2010 16:19:26 IST

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Since the greatest integer function is associated, let's just deal with the limit from the left hand site and the right hand site.

From the RHL, Sinx/x is a little less than 1, or as we say --> 1-. Hence the greatest integer value is 0.

From the LHL, sinx/x is a little greater than 1, or as we say --> 1+. Hence the greatest integer value is 1.

So, we see, that the two limits do not mtch and hence the limit does not exist.

Dharav Solanki

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1 Jan 2010 16:21:15 IST

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I have left it upto you to arrive at the conclusion as to how I derived the LHL and the RHL. You can graph y = sinx and y = x and se that on the RHS of zero, y=x is on top of the sine curve; while the reverse is true for the curve on the LHS of zero.

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