IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

ashish_banga

let the function

$F(x) = 4sinx + 3cosx + log ( |x| + \sqrt{1 + {x}^{2}}$ )

be defined on the interval [0 ,1] . the odd extension of F(x) on the interval [ -1 , 1 ] is

ashish_banga

anyone here

spideyunlimited

G(x) = { - F(-x) -1<= x < 0
{ F(x) 0<= x <= 1

where G(x) is the odd extension .... I just had to look up on the net about odd extensions.

WHERE
- F(-x) = - [ -4sinx + 3cosx + log (|x| + sqrt ( 1 + x^2 ) ]
= 4 sin x - 3 cos x - log (|x| + sqrt (1 + x^2) ]

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