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Differential Calculus

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11 Jun 2007 17:43:04 IST

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1119

the easiest I could GIve

None

_[x_]

_[0] xtan2x - 2xtanx I need the soln don't guess

(1 - cos2x)²

a)2

b) -2

c)1/2

d)-1/2

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Comments (11)

rahul batra

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11 Jun 2007 17:48:51 IST

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answer is a)2

rahul batra

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11 Jun 2007 17:51:23 IST

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denominator becomes sinx^4.
u can take x common from num. and cancel with the sinx in den.
now left with (tan2x-2tanx)/sin^3x.
apply tan2x=2tanx/(1-tan^2x).
n solve it.

rahul batra

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11 Jun 2007 18:16:24 IST

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is the answer correct?

rahul batra

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11 Jun 2007 18:19:10 IST

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helllooooooooooo.anybody....

nishant dash

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11 Jun 2007 18:48:10 IST

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in the numerator,write tan2x as 2tanx/1+tan^2x....then take 2xtanx common from the numerator....u will be left with _{[ x]}

_{[ 0]} 2xtanx.(1/1+tan^2x-1)/(1-cos2x)^2....if u simplify the numerator further u will be left with 2xtanx. - tan^2x...in denominator,substitute 2sin^2x in place of 1-cos2x...as we know that cos2x=1-2sin^2x...u will get 4sin^4x.sec^2x in denominator...now write tan^2x in numerator as sin^2x/cos^2x..cancel sin^2x from both numerator and denominator .also cancel 2 and 4..u will be left with lim x tends to 0 - xtanx/2sin^2x...this is of 0/0 form..so apply l'hospital rule...u will have to apply it 2 times...the final answer is -1/2....hope u got it...cheers..

waterdemon

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11 Jun 2007 19:12:26 IST

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dude first you know that sinx/x is nothing but 1. after you take "x" common you will get
tan2x - 2tanx/4sin^3 x and then apply formula for tan2x
that is

2tanx/1-tan^2 x
then
u will get 2tanx commom
with tan^2x left common inside

atlast
it will be
2tanx * tan^2x/4sin^3 x
place value of tanx and then u will get

1 / 2.cosx.cos^2 x
ans is 1/2 if u place the value of x=o in the given equation
you must have solved it.

aravindh ramaswamy

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11 Jun 2007 19:55:58 IST

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We can try the L'Hospital rule,can't we for that sum?

nishant dash

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12 Jun 2007 08:29:32 IST

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both of u are correct waterdemon and aravindh,i mistakenly wrote tan2x as 2tanx/1+tan^2xwhich is actually sin2x......the l'hsptl rule can be applied as it comes out to be of 0/0 form after cancelling...so answer is 1/2...cheeers..

Prabhas Bajaj

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12 Jun 2007 23:15:58 IST

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expand tan2x using tan(a+b) formula
then write 1- cos2x in terms of tan using formula- cos2x= 1- tan^2(x) (^2= sqr)
1+tan^2(x)
cancel all terms including tan
simplify nd solve

u"ll get final term as sec^4x
2cos2x

Thus, answer is 1/2

Priyak Dey

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3 Oct 2009 01:07:33 IST

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The ans is -1/2..........................

is it brother.......n ur ques abt d cube was damn gud......

BT PLZ CAN U GIV A MORE CLEAR PIC PLZZZ..................LUKING FRWD FOR UR HLP...............

Priyak Dey

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3 Oct 2009 01:09:30 IST

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SORRY D ANS IS 1/2..........

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