What is the limit as x approaches 4 of (x^3-8x^2+18x-8)/(x-4) ?

The limit as x approaches 4 of (x^3-8x^2+18x-8)/(x-4) is 2

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limit as x approaches 4 of (x^3-8x^2+18x-8)/(x-4)

x \to 4 lim (\frac{x ^{3} - 8 x ^{2} + 18 x - 8}{x - 4})

2

Solution steps

x \to 4 lim (\frac{x ^{3} - 8 x ^{2} + 18 x - 8}{x - 4})

Simplify

\frac{x ^{3} - 8 x ^{2} + 18 x - 8}{x - 4} : x^{2} - 4 x + 2

= x \to 4 lim (x^{2} - 4 x + 2)

Plug in the value

x = 4

= 4^{2} - 4 \cdot 4 + 2

Simplify

= 2

x \to 0 - lim (\frac{1}{cos ( x )})

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

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

x \to 3 + lim (\frac{7 x - 5}{x - 3})

x \to 4 lim (\frac{3 x - 1}{x - 4})

What is the limit as x approaches 4 of (x^3-8x^2+18x-8)/(x-4) ?
The limit as x approaches 4 of (x^3-8x^2+18x-8)/(x-4) is 2