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" (i) "quad x sin x^(2)...

" (i) "quad x sin x^(2)

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"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

int (cos^(2)x+sin 2x)/((2 cos x- sin x)^(2))dx

int (cos^(2)x+sin 2x)/((2 cos x- sin x)^(2))dx

lim_ (x rarr oo) (x ^ (2) (1 + sin ^ (2) x)) / ((x + sin x) ^ (2))

The number of solution x of the equation sin (x+x^(2))- sin(x^(2))= sin x in the interval [2,3] is

(sin x - sin 3x)/( sin ^(2) x - cos ^(2) x) = 2 sin x

(sin x - sin 3x)/( sin ^(2) x - cos ^(2) x) = 2 sin x