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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow 0}\left(\frac{\sin a x}{\tan b x}\right)\) is equal to

  1. A \(a b\)
  2. B \(\frac{a}{b}\)
  3. C \(\frac{b}{a}\)
  4. D 1
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{a}{b}\)

Step-by-step Solution

Detailed explanation

\(\lim _{x \rightarrow 0}\left(\frac{\sin a x}{\tan b x}\right)\) \[ \lim _{x \rightarrow 0} a\left(\frac{\sin a x}{a x}\right) \times \lim _{x \rightarrow 0} \frac{1}{\left(\frac{\tan b x}{b x}\right) b}=a \times \frac{1}{b}=\frac{a}{b} \]