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Evaluate the Following Limit: Lim H → 0 ( a + H ) 2 Sin ( a + H ) − a 2 Sin a H

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Question

Evaluate the following limit: 

\[\lim_{h \to 0} \frac{\left( a + h \right)^2 \sin\left( a + h \right) - a^2 \sin a}{h}\] 

Sum
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Solution

\[\lim_{h \to 0} \frac{\left( a + h \right)^2 \sin\left( a + h \right) - a^2 \sin a}{h}\] 
f'(x) = `lim_("h"->0) (f(x + "h") - f(x))/"h"`
f(x) = x2sinx
f'(x) = 2xsinx + x2cosx
= x [2sinx + xcosx]
= a [2sina + acosa]
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Chapter 29: Limits - Exercise 29.7 [Page 51]

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R.D. Sharma Mathematics [English] Class 11
Chapter 29 Limits
Exercise 29.7 | Q 62 | Page 51

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