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What is the limit of #sqrt(x^3-2x^2+1)/[x-1]# as x goes to infinity?

Answer 1

Ezra Adams

#lim_(xrarroo)sqrt(x^3-2x^2+1)/(x-1) = oo#

#sqrt(x^3-2x^2+1) = sqrt(x^2(x-2+1/x^2))#

# = sqrt(x^2)sqrt(x-2+1/x^2)#

# = absx sqrt(x-2+1/x^2)#

#lim_(xrarroo)sqrt(x^3-2x^2+1)/(x-1) = lim_(xrarroo)(absx sqrt(x-2+1/x^2))/(x(1-1/x))#

# = lim_(xrarroo)(sqrt(x-2+1/x^2))/(1-1/x)#

# = oo#

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Answer 2

Evelyn Agard

The limit of sqrt(x^3-2x^2+1)/[x-1] as x goes to infinity is infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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