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How do you integrate #y=(x^(7/5)-x^(8/5))/root5x# using the quotient rule?

Answer 1

Christopher Allers

There is no quotient rule for integrating.

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Answer 2

Evelyn Agard

To integrate y = (x^(7/5) - x^(8/5)) / sqrt(5x) using the quotient rule, you can rewrite the expression as follows:

y = (1/sqrt(5x)) * (x^(7/5) - x^(8/5))

Now, let u = x^(7/5) - x^(8/5) and v = sqrt(5x). Applying the quotient rule:

y' = (u'v - uv') / v^2

Where: u' = (7/5)x^(2/5) - (8/5)x^(3/5) v' = (1/2)(5x)^(-1/2)

Substituting these values into the quotient rule formula:

y' = [(7/5)x^(2/5) - (8/5)x^(3/5)]*sqrt(5x) - (x^(7/5) - x^(8/5)) * (1/2)(5x)^(-1/2) / (5x)

Simplify the expression to obtain the final result.

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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.