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How do you determine the limit of #(3/x^3 - 6/x^6)# as x approaches 0-?

Answer 1

Scarlett Allison

#3/x^3-6/x^6 = (3x^3-6)/x^6#

So the limit is #-oo# (Doe not exist because as #xrarr0^-#,

#(3x^3-6)rarr-6#

and #x^6rarr0^+#

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Answer 2

Axel Alvarez

To determine the limit of (3/x^3 - 6/x^6) as x approaches 0-, we can simplify the expression by finding a common denominator. The common denominator is x^6.

By multiplying the first term by x^3/x^3 and the second term by x^6/x^6, we get (3x^3/x^6 - 6/x^6).

Combining the terms, we have (3x^3 - 6) / x^6.

As x approaches 0-, the numerator approaches -6, and the denominator approaches 0.

Therefore, the limit of (3/x^3 - 6/x^6) as x approaches 0- is -∞.

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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.