Calculus - Values of m

1

injun joe ·2009-09-05 06:27:26

Plzzz try...

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injun joe ·2009-09-07 23:16:09

????

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Arshad ~Died~ ·2009-09-07 23:18:05

arrey we want some expert opinion.........

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Manish Shankar ·2009-09-07 23:30:52

(1-cosx)/x^m=2sin²(x/2)/x^m

So at xâ†’0 find the value of m for limit to exist

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Arshad ~Died~ ·2009-09-07 23:32:35

sir we are not able to solve further...can u pls post the full solution...

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Manish Shankar ·2009-09-07 23:40:42

2sin²(x/2)/x².1/x^m-2

2sin²(x/2)/4(x/2)².1/x^m-2

f(x)=1/2.sin²(x/2)/(x/2)².1/x^m-2

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Arshad ~Died~ ·2009-09-07 23:41:14

value of m can be 2

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Arshad ~Died~ ·2009-09-07 23:42:05

can anyone explain in detail what does converging of an integral mean..?

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injun joe ·2009-09-07 23:43:02

@ Manish sir. By what I gather,

âˆ«(from -âˆž to âˆž) f(x)dx = lim Aâ†’-âˆžâˆ«(from A to C) f(x)dx + lim Bâ†’âˆžâˆ«(from C to B) f(x)dx

If the upper limits exist and are finite, the appropriate integral is convergent.

Am I correct?

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injun joe ·2009-09-07 23:45:11

m<3

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Manish Shankar ·2009-09-07 23:58:14

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Manish Shankar ·2009-09-08 00:00:10

But as far as I know convergence is not in the syllabus of IITJEE

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Arshad ~Died~ ·2009-09-08 06:14:59

thanks sir...

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Values of m

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