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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=32) a=c=13) a+b+c+d=24) noneMore than one correct

Jitender Singh IIT Delhi
6 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