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Question Number 170057 by nimnim last updated on 15/May/22

$$\underset{x\to 0}{lim}\frac{x}{a}\lfloor \frac{b}{x}\rfloor wherea,b>0$$ $$please....$$

Answered by mahdipoor last updated on 15/May/22

$$get\frac{b}{x}=t$$ $$\underset{x\to 0}{\lim }\frac{x}{a}\left[\frac{b}{x}\right]=\underset{x\to 0}{\lim }\frac{b}{a}\times \frac{\left[\frac{b}{x}\right]}{\frac{b}{x}}=\frac{b}{a}\underset{t\to \pm \mathrm{\infty }}{\lim }\frac{\left[t\right]}{t}=\frac{b}{a}$$

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