LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES2 Marks
Question
Evaluate $\lim \limits_{x \rightarrow 0} \frac{\sin a x}{b x}$
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Answer
Given, $\lim _{x \rightarrow 0} \frac{\sin a x}{b x}$ $$Applying the limits in the given expression we get,$\lim _{x \rightarrow 0} \frac{\sin a x}{b x}=\frac{0}{0}$ Multiplying and dividing the given expression by a we get, $\Rightarrow \lim _{x \rightarrow 0} \frac{\sin a x}{b x} \times \frac{a}{a}$ $\Rightarrow \lim _{x \rightarrow 0} \frac{\sin a x}{a x} \times \frac{a}{b}$ We know that: $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$ $= \frac{a}{b} \lim _{a x \rightarrow 0} \frac{\sin a x}{a x}=\frac{a}{b} \times 1=\frac{a}{b}$
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