How do you find the limit of #(3x-3) /( x^4 - 12x^3 + 36x^2)# as x approaches #3^+#?

Answer 1

Charles Arocha

#= 2/ 27#

#lim_{x to 3^+} (3x-3) /( x^4 - 12x^3 + 36x^2)#

#= lim_{x to 3^+} 1/x^2 * lim_{x to 3^+} (3(x-1)) /( x^2 - 12x + 36)#

#= 1/9 * lim_{x to 3^+} (3(x-1)) /( x-6)^2#

#= 1/9 * (3(3-1)) /( 3-6)^2#

#= 2/ 27#

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Answer 2

Emily Ammerman

To find the limit of (3x-3) /( x^4 - 12x^3 + 36x^2) as x approaches 3^+, we can substitute the value of 3 into the expression. By plugging in 3 for x, we get (3(3)-3) /( 3^4 - 12(3)^3 + 36(3)^2), which simplifies to 6/0. Since the denominator is zero, the limit does not exist.

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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.