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Popular Calculus >

limit as x approaches 1 of \sqrt[3]{(x^3-1)/(x^2-3x+2)}

Solution

x \to 1 lim (3 \frac{x ^{3} - 1}{x ^{2} - 3 x + 2})

Solution

3 - 1 33

Solution steps

x \to 1 lim (3 \frac{x ^{3} - 1}{x ^{2} - 3 x + 2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= 3 x \to 1 lim (\frac{x ^{3} - 1}{x ^{2} - 3 x + 2})

Simplify

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

= 3 x \to 1 lim (\frac{x ^{2} + x + 1}{x - 2})

Plug in the value

x = 1

= 3 \frac{1 ^{2} + 1 + 1}{1 - 2}

Simplify

3 \frac{1 ^{2} + 1 + 1}{1 - 2} : 3 - 1 33

= 3 - 1 33

Graph

Popular Examples

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x \to - 1 lim (\frac{2 x + 3}{x + 1})

integral from 0 to 6 of 1/((x-4)^{2/3)}

\int_{0}^{6} \frac{1}{( x - 4 ) ^{\frac{2}{3}}} d x

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\int \frac{5 x ^{4} + 4}{x ^{5} + 4 x} d x

integral from 0 to pi/4 of sec^2(t)

\int_{0}^{\frac{π}{4}} sec^{2} (t) d t

(dy)/(dx)=(1-2x)/(4x-x^2)

\frac{d y}{d x} = \frac{1 - 2 x}{4 x - x ^{2}}

Frequently Asked Questions (FAQ)

What is the limit as x approaches 1 of \sqrt[3]{(x^3-1)/(x^2-3x+2)} ?
The limit as x approaches 1 of \sqrt[3]{(x^3-1)/(x^2-3x+2)} is cube root of-1}\sqrt[3]{3