MCQ
$\mathop {\lim }\limits_{h \to 0} \frac{{{{(a + h)}^2}\sin (a + h) - {a^2}\sin a}}{h} = $
- A$a\cos a + {a^2}\sin a$
- B$a\sin a + {a^2}\cos a$
- ✓$2a\sin a + {a^2}\cos a$
- D$2a\cos a + {a^2}\sin a$
Aliter : Apply $ L-$ Hospital’s rule,
$\mathop {\lim }\limits_{h \to 0} \,\frac{{{{(a + h)}^2}\sin (a + h) - {a^2}\sin a}}{h}$
$ = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{2\,(a + h)\,\sin \,(a + h) + {{(a + h)}^2}\cos \,(a + h)}}{1}$
$ = 2a\,\,\sin a + {a^2}\cos \,\,a.$
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