Find the limits. \lim_{x \rightarrow -\infty}\sqrt{\frac{x^{2}-5x}{x^{3}+x-2}}

aortiH

aortiH

Answered question

2021-09-14

The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits.
limxx25xx3+x2

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2021-09-15Added 96 answers

Divide both numerator and denominator with x3
limxx25xx3+x2:x3x3=limx1x5x21+1x22x3=
Now since square root is continuous function, limit can "go under" the root. First calculate limit of fraction under root and then take square root of result.
limxaxn=0
=001+00=0=0

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