What is the limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3) ?

The limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3) is 1/12

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limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3)

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})

\frac{1}{12}

Decimal

0.08333 \dots

Solution steps

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})

Simplify

\frac{x - 2 y}{x ^{3} - 8 y ^{3}} : \frac{1}{x ^{2} + 2 x y + 4 y ^{2}}

= (x, y) \to (2, 1) lim (\frac{1}{x ^{2} + 2 x y + 4 y ^{2}})

Plug in the value

(x, y) = (2, 1)

= \frac{1}{2 ^{2} + 2 \cdot 2 \cdot 1 + 4 \cdot 1 ^{2}}

Simplify

\frac{1}{2 ^{2} + 2 \cdot 2 \cdot 1 + 4 \cdot 1 ^{2}} : \frac{1}{12}

= \frac{1}{12}

What is the limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3) ?
The limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3) is 1/12