Evaluate the Given limit:\(\lim\limits_{x \to 0} \dfrac{sinax}{bx}\)

Asked by Abhisek | 11 months ago |  61

1 Answer

Solution :-

\( \lim\limits_{x \to 0} \dfrac{sinax}{bx}\)

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

Now,

\( \lim\limits_{x \to 0} \dfrac{sin\;ax}{bx}\)

\( \lim\limits_{x \to 0} \dfrac{sin\;ax}{ax}\times \dfrac{ax}{bx}\)

\( \lim\limits_{x \to 0} \dfrac{sin\;ax}{ax}\times \dfrac{a}{b}\)

\(\dfrac{a}{b} \lim\limits_{ax \to 0} \dfrac{sin\;ax}{ax} \)

\( \dfrac{a}{b}\times 1\)

\( \dfrac{a}{b}\)

Answered by Pragya Singh | 11 months ago

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