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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 .
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Analytical Geometry

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

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

Blazing goIITian

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

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..

Forum Expert
Joined: 23 Oct 2009
Posts: 580
14 Dec 2009 18:30:01 IST
1 people liked this

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

Blazing goIITian

Joined: 6 May 2008
Posts: 386
15 Dec 2009 20:16:20 IST
0 people liked this

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

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