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How do you determine the limit of #(3/x^3) ((x-2)/(x-1))# as x approaches 1-?

Answer 1

Evelyn Agard

#lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo#

#lim_(xrarr1^(-))(3(x-2))/(x^3(x-1))=#

#lim_(xrarr1^(-))3/x^3*((x-2)/(x-1))=-oo#

because

#x->1^-# #<=># #x-1<0# so #lim_(xrarr1^(-))1/(x-1)=^((1/0^(-)))=-oo#

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Answer 2

Ezra Adams

To determine the limit of the given expression as x approaches 1-, we can simplify the expression and substitute the value of x into it.

First, simplify the expression: (3/x^3) * ((x-2)/(x-1)) = (3(x-2))/(x^3(x-1))

Next, substitute x = 1 into the simplified expression: (3(1-2))/(1^3(1-1)) = (-3)/(0)

Since we have a denominator of 0, the expression is undefined. Therefore, the limit does not exist as x approaches 1-.

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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.