Evaluate `lim_(h to 0) ((a+h)^(2) sin (a+h) -a^(2) sin a)/h `.

1.	Evaluate `lim_(h to 0) ((a+h)^(2) sin (a+h) -a^(2) sin a)/h `.
Answer» Correct Answer - `a^(2) cos alpha + 2a sin alpha` Here, ` underset( h to 0) lim ((a+h)^(2) sin (a+h)-a^(2) sin a)/h` ` underset( h to 0) lim(a^(2)[sin (a+h)-sin a])/h` `+(h[2a sin (a+h)+h sin (a+h)])/h ` ` = underset( h to 0) lim (a^(2)2 cos(a+h/2) sin h/2)/(2*h/2) + (2a+h) sin (a+h) ` ` = a^(2) cos a + 2a sin a`

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