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Lim X → 0 Log ∣ ∣ 1 + X 3 ∣ ∣ Sin 3 X - Mathematics

\[\lim_{x \to 0} \frac{\log \left| 1 + x^3 \right|}{\sin^3 x}\] 

 

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Solution

\[\lim_{x \to 0} \left[ \frac{\log \left( 1 + x^3 \right)}{\sin^3 x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\log \left( 1 + x^3 \right)}{x^3} \times \frac{x^3}{\sin^3 x} \right]\]
\[ = 1 \times \frac{1}{1^3}\]
\[ = 1\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 27 | Page 71
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