What is the limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3) ?

The limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3) is 1/(7a)

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limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3)

x \to 2 a lim (\frac{x ^{2} - 2 a x + a ^{2}}{x ^{3} - a ^{3}})

\frac{1}{7 a}

Solution steps

x \to 2 a lim (\frac{x ^{2} - 2 a x + a ^{2}}{x ^{3} - a ^{3}})

Plug in the value

x = 2 a

= \frac{( 2 a ) ^{2} - 2 a \cdot 2 a + a ^{2}}{( 2 a ) ^{3} - a ^{3}}

Simplify

\frac{( 2 a ) ^{2} - 2 a \cdot 2 a + a ^{2}}{( 2 a ) ^{3} - a ^{3}} : \frac{1}{7 a}

= \frac{1}{7 a}

\int_{2}^{4} 3 x d x

\frac{\partial}{\partial x} (arctan (2 x))

x \to - 1 lim (- 1 (x + 1))

\frac{d}{d x} (7 x + 3)

\frac{d}{d x} (- \frac{192}{x ^{4}})

What is the limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3) ?
The limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3) is 1/(7a)