Use the Error Bound formula for the Trapezoidal Rule to determine N so that if ∫ from 10 to 0 e^2x dx is approximated using the Trapezoidal Rule with N subintervals, the error is guaranteed to be less than 10^4.

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step-by-step explanation:

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, and

for

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we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation: