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How do you find the limit of #(4x² -2x^15 +17)/(3x^6 - 7x^3 + 216)# as x approaches infinity?

Answer 1

Christopher Agresta

#-oo#

Divide the numerator and denominator by #x^6#,the given expression would become

#((4/x^4 -2x^9 +17/x^6))/(3-7/x^3 +216/x^6)#

Now apply the limit #x->oo#, it would become #-oo/3#= #-oo#

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Answer 2

Ezra Adams

To find the limit of the given expression as x approaches infinity, we need to examine the highest power terms in the numerator and denominator. In this case, the highest power terms are x^15 in the numerator and x^6 in the denominator.

Since the power of x in the numerator is greater than the power of x in the denominator, as x approaches infinity, the numerator will dominate the denominator.

Therefore, the limit of (4x² -2x^15 +17)/(3x^6 - 7x^3 + 216) as x approaches infinity is positive 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.