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How do you integrate #g(t)=t^2-4/t# using the power rule?

Answer 1

Emma Aldridge

The derivative of the function is #g'(t)=2t+4/t^2#

The power rule states that the derivative of #f(t)=t^n# is #f'(t)=nt^(n-1)#.

Rewrite the function with a negative exponent:

#g(t)=t^2-4t^-1#

Now apply the power rule:

#g'(t)=2t^(2-1)-4(-1)t^(-1-1)#

#g'(t)=2t^1+4t^-2#

#g'(t)=2t+4/t^2#

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Answer 2

Charles Arocha

To integrate ( g(t) = \frac{t^2 - 4}{t} ) using the power rule, first, split the fraction into two separate terms: ( g(t) = t - \frac{4}{t} ). Then, integrate each term separately. The integral of ( t ) with respect to ( t ) is ( \frac{1}{2}t^2 ), and the integral of ( \frac{4}{t} ) is ( 4 \ln|t| ). So, the integral of ( g(t) ) is ( \frac{1}{2}t^2 + 4 \ln|t| + C ), where ( C ) is the constant of integration.

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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.