21-06-2021
Mathematics

contestada

lim x->0 [ (x^2 - 2x) / (x^3 - 4x) ]

Find this limit’s value.

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LammettHash LammettHash

25-06-2021

Cancel the factor of x in both the numerator and denominator to get a limand that is continuous at 0:

[tex]\displaystyle\lim_{x\to0}\frac{x^2-2x}{x^3-4x} = \lim_{x\to0}\frac{x-2}{x^2-4} = \frac{0-2}{0^2-4} = \boxed{\dfrac12}[/tex]

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