Evaluate the given limit: $$\lim\limits_{x \to 0} \dfrac{sinax}{sinbx},a,b\neq 0$$

Asked by Abhisek | 1 year ago |  66

Solution :-

$$\lim\limits_{x \to 0} \dfrac{sinax}{sinbx},a,b\neq 0$$

At x = 0, the value of the given function takes the form $$\dfrac{0}{0}$$

$$\lim\limits_{x \to 0} \dfrac{\dfrac{sinax}{ax}\times ax}{\dfrac{sin\;bx}{ax}\times bx}$$

$$\dfrac{a}{b}\times \dfrac{ \lim\limits_{ax \to 1}\dfrac{sinax}{ax}}{ \lim\limits_{bx \to 1} \dfrac{sin\;bx}{ax}}$$

$$\dfrac{a}{b}\times \dfrac{1}{1}$$

$$\dfrac{a}{b}$$

Answered by Pragya Singh | 1 year ago

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