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Chapter 1: Q. 23 (page 153)

Find the limit by hand.
$\lim_{x \to 0} \frac{3 x}{\sin 2 x}$

Short Answer

Expert verified

On solving the limit, we get, $\infty$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\lim_{x \to 0} \frac{3 x}{\sin 2 x}$

Step 2. Solve the given limit.

Using the quotient rule,

$= \frac{\lim_{x \to 0} 3 x}{\lim_{x \to 0} \sin 2 x} = \frac{3 (0)}{\sin (2 \cdot 0)} = \frac{0}{\sin 0} = \frac{0}{0} = \infty$

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$\lim_{x \to - 3} (1 - x) = 4$ .

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Find the limit by hand.limx→03xsin2x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the given limit.

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Find the limit by hand.
$\lim_{x \to 0} \frac{3 x}{\sin 2 x}$