What is the limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3) ?

The limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3) is a/c

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limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3)

x \to 0 lim (\frac{a x ^{2} + b x ^{3}}{c x ^{2} + d x ^{3}})

\frac{a}{c}

Solution steps

x \to 0 lim (\frac{a x ^{2} + b x ^{3}}{c x ^{2} + d x ^{3}})

Simplify

\frac{a x ^{2} + b x ^{3}}{c x ^{2} + d x ^{3}} : \frac{a + b x}{c + d x}

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

Plug in the value

x = 0

= \frac{a + b \cdot 0}{c + d \cdot 0}

Simplify

= \frac{a}{c}

What is the limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3) ?
The limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3) is a/c