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GATE2014-1-46
14
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2.3k
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The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$. The value of $t$ is______.
gate2014-1
calculus
easy
numerical-answers
differentiation
asked
Sep 28, 2014
in
Calculus
jothee
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Jun 20, 2017
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Silpa
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Best answer
$f'(x) =x\cos(x) + \sin(x)$
$f''(x)=x(-\sin x) +\cos x +\cos x$
now $f''(x)+f(x)+t \cos x= 0$
$ \Rightarrow x(-\sin x)+\cos x+\cos x+x\sin x+t\cos x=0$
$\Rightarrow 2\cos x+t\cos x = 0$
$\Rightarrow \cos x(t+2)=0$
$\Rightarrow t+2=0, t=-2$
answered
Jul 8, 2015
saket nandan
edited
Nov 27, 2017
by
pavan singh
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5
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Hence, t = -2
answered
Jul 9, 2017
tvkkk
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2
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t=-2
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Jan 15, 2015
aditi
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1
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We have f(x) = x sin x
β f'(x) = x cos x + sin x
β fβ²β²(x) = x (β sin x ) + cos x + cos x = (βx sin x ) + 2 cos x
Now, it is given that f(x) = x sin x satisfies the equation fβ²β²(x) + f(x) + t cos x = 0
β (βx sin x ) + 2 cos x + x sin x + t cos x = 0
β 2 cos x + t cos x = 0
β cos x ( t + 2 ) = 0
β t + 2 = 0
β t = β2
answered
Apr 7, 2017
Regina Phalange
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β Prev.
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β Prev. Qn. in Sub.
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Answer:
-2
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