Alicia can walk 1/4 mile every 1/5 hour. At this rate, how far can Alicia walk in one hour?
1 answer:
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Answer:
(a) B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
(b) Every function of the form is an antiderivative of 8x
Step-by-step explanation:
A function <em>F </em>is an antiderivative of the function <em>f</em> if
for all x in the domain of <em>f.</em>
(a) If , then
is an antiderivative of <em>f </em>because
Therefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of <em>f</em>.
(b) Because
then is an antiderivative of
. Therefore, every antiderivative of 8x is of the form
for some constant C, and every function of the form
is an antiderivative of 8x.
This appears to be just an expression we are simplifying, not an equation we are solving. I THINK you are saying that the expression looks like this:
If you rationalize the denominator, you would get this expression:
which, after simplifying, looks like this:
and that's as simple as I can see that one getting. You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!
If you rationalize the denominator, you would get this expression:
which, after simplifying, looks like this:
and that's as simple as I can see that one getting. You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!