= (a^2+2ah + h^2)(sin (a+h) – a^2 ain a

= a^2( sin (a+h) – sin a)) + (2ah + h^2)(sin (a+h))

= a^2 ( sin a cos h + cos a sin h – sin a) + (2ah + h^2)(sin (a+h))

= a^2 ( sin a (cos h – 1) + cos a sin h) + (2ah + h^2)(sin (a+h))

so given expression deviding by h

= (a^2 ( sin a (cos h – 1) + cos a sin h) + (2ah + h^2)(sin (a+h))(/h

= a^2( sin a (cos h-1)/h + cos a sin h/h ) + (2a+h) sin (a+h))

= a^2( sin a (- 2 sin ^2 h/2)/h + cos a sin h/h ) + (2a+h) sin (a+h))

as h->0 we have sinh/h = 1 and (sin ^2 h/2)/h = 2 ( sin h/2)( sin h/2)/h = 0 and sin (a+h) = sin a giving

a^2 cos a + 2a sin a that is the limit

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