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Analytical Geometry

Scorching goIITian

Joined:	18 Nov 2007
Post:	287

14 Dec 2009 17:29:20 IST

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lim x-> 0 (xtan2x - 2xtanx ) / (1-cos2x)^2 Answer : 1/2 .

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lim x-> 0 (xtan2x - 2xtanx ) / (1-cos2x)^2Answer : 1/2 .

Comments (5)

umesh

Forum Expert

Joined: 23 Oct 2009

Posts: 580

14 Dec 2009 18:03:36 IST

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(1-cos2x)^1/2 =root(2) sinx

now

xtan2x -2xtanx = 2x( x(tan2x/2x) -x(tanx/x))

when x tending to 0

tan A/A tending to 1

hence

2x( x(tan2x/2x) -x(tanx/x)) = 2x²

given problem

2x²/root(2) sinx = root(2)x/(sinx/x)

hence root(2) x

hence 0

eragon24

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Joined: 14 May 2009

Posts: 697

14 Dec 2009 18:10:23 IST

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using expansion of tan x and sin x

umesh

Forum Expert

Joined: 23 Oct 2009

Posts: 580

14 Dec 2009 18:27:38 IST

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But I am not getting error in my solution..someone plzz give me explanation why can't it solve by my method..

umesh

Forum Expert

Joined: 23 Oct 2009

Posts: 580

14 Dec 2009 18:30:01 IST

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got it

I have taken (1-cos2x)^(1/2) rather it would be (1-cos2x)^2

now

xtan2x -2xtanx = 2x( x(tan2x/2x) -x(tanx/x))

when x tending to 0

tan A/A tending to 1

hence

2x( x(tan2x/2x) -x(tanx/x)) = 2x²

given problem

2x²/4 sin^2x = 1/2

akl

Blazing goIITian

Joined: 6 May 2008

Posts: 386

15 Dec 2009 20:16:20 IST

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well i m unable to rem exp,...does it needed

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