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Trigonometry

Q(d). Edward, a student, decides to use this method to find a more accurate value for the
integral by increasing the number of terms of the binomial expansion used.
Explain clearly whether Edward’s approximation will be an overestimate, an
underestimate, or if it is impossible to tell.

The previous questions was finding the integral of a binomial expansion - integral of (4 - x^3)^-0.5.
I don't understand how increasing the number of terms will lead to an overestimate or underestimate of the area I got from integrating, and which topic is this under? How should I study this?
Does anyone know the answer? Please help.

Also, when you integrate and the number in the top of the integral is 0 and the number at bottom of the integral is -2, then why would the approximation be invalid?? Is it because the area would be negative...?
Thank you.

I have another question.
Q. A scientist is researching the effects of caffeine. She models the mass of caffeine in
the body using:
m = m0*e^(-kt).

where m0 milligrams is the initial mass of caffeine in the body and m milligrams is the
mass of caffeine in the body after t hours.
On average, it takes 5.7 hours for the mass of caffeine in the body to halve.
One cup of strong coffee contains 200 mg of caffeine.

(a) The scientist drinks two strong cups of coffee at 8 am. Use the model to estimate the
mass of caffeine in the scientist’s body at midday.
(b) The scientist wants the mass of caffeine in her body to stay below 480 mg
Use the model to find the earliest time that she could drink another cup of strong
coffee.
Give your answer to the nearest minute.

I get how to do (a),
but I don't understand how to do (b) - I'm keep getting a negative number for time(t) however I calculate it.
Can anyone show me the answer step by step?
Thank you.
Original post by ChloeYeo
Q(d). Edward, a student, decides to use this method to find a more accurate value for the
integral by increasing the number of terms of the binomial expansion used.
Explain clearly whether Edward’s approximation will be an overestimate, an
underestimate, or if it is impossible to tell.

The previous questions was finding the integral of a binomial expansion - integral of (4 - x^3)^-0.5.
I don't understand how increasing the number of terms will lead to an overestimate or underestimate of the area I got from integrating, and which topic is this under? How should I study this?
Does anyone know the answer? Please help.

Also, when you integrate and the number in the top of the integral is 0 and the number at bottom of the integral is -2, then why would the approximation be invalid?? Is it because the area would be negative...?
Thank you.


Topic is binomial expansions.

Look at the terms in your expansion. As you add more terms are the partial sums increasing, decreasing, or neither of those. Hence what can you say about the estimate of the area as the number of terms increases?

Integral. What's the valid range for the binomial expansion? Hence....


Coffee. Consider:

Since one cup contains 200 mg, what level must her body be at at most, if when she drinks it she stays below 480mg?
So, how long does it take for her body to come down to that level, having drunk the 2 cups earlier?
Then what time would that be?

Since you're getting a negative number, I suspect you've probably missed a sign at some point. If you can't find the error, post your working. NOTE: It's against forum rules to give a fully worked solution.
(edited 4 years ago)

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