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If f (x) = (ax+b) sinx + (cx+d) cosx where a, b, c, d belongs to R is such that f'(x) = xcosx for all x then 1) a+2d=3 2) a=c=1 3) a+b+c+d=2 4) none More than one correct

If f (x) = (ax+b) sinx + (cx+d) cosx where a, b, c, d belongs to R is such that f'(x) = xcosx for all x then 
1) a+2d=3
2) a=c=1
3) a+b+c+d=2
4) none
More than one correct
 

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans: (1) & (3)
f(x) = (ax+b)sinx + (cx+d)cosx
f'(x) = (ax+b)cosx+asinx + (cx+d)(-sinx)+c.cosx = x.cosx(ax+b+c)cosx+(a-cx-d)sinx = x.cosx
(a-1)x + b + c = 0
cx - a +d=0
Sice x belong to R
a-1 = 0
a=1
c = 0
d = a =1
b = c = 0
a + 2d = 1 + 2(1) = 3
a +b+c+ d = 1 + 0 + 0 + 1 = 2
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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