What is the limit as x approaches 0 of [ x/a ]*b/x ?

The limit as x approaches 0 of [ x/a ]*b/x is b/a

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limit as x approaches 0 of [ x/a ]*b/x

x \to 0 lim ([\frac{x}{a}] \cdot \frac{b}{x})

\frac{b}{a}

Solution steps

x \to 0 lim ([\frac{x}{a}] \frac{b}{x})

Simplify

[\frac{x}{a}] \frac{b}{x} : \frac{b}{a}

= x \to 0 lim (\frac{b}{a})

x \to a lim c = c

= \frac{b}{a}

x \to 0 lim ([\frac{1}{x} - \frac{1}{ln ( 1 + x )}])

x \to - 2 - lim (\frac{2 - ∣ x ∣}{2 + x})

x \to 0 lim (\frac{sin ( x ) + x}{x})

x \to 0 + lim (2 x csc (2 π - x))

x \to 2 lim (4 - 2 x)

What is the limit as x approaches 0 of [ x/a ]*b/x ?
The limit as x approaches 0 of [ x/a ]*b/x is b/a