Question

2. In this problem we will see how to use Riemann Sums to calculate ln(2). (a) According to the Fundamental Theorem of Calculus which bound b is needed to get ?_1^b 1/x dx = ln(2)? Show your work. (b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5 rectangles with equal bases. Is this an over or an under estimate? (c) Give a clear explanation of how to estimate/calculate ln(2) to within an accuracy of ?, for example, ? = 0.01. Specifically how many subdivisions are needed? (d) With n = 5 compare the left endpoint approximation L_5, the right endpoint approximation R_5 and their average to ln(2) (use a calculator.) Which is best?

          2. In this problem we will see how to use Riemann Sums to calculate ln(2).
(a) According to the Fundamental Theorem of Calculus which bound b is needed to get
?_1^b 1/x dx = ln(2)? Show your work.
(b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5
rectangles with equal bases. Is this an over or an under estimate?
(c) Give a clear explanation of how to estimate/calculate ln(2) to within an accuracy of ?,
for example, ? = 0.01. Specifically how many subdivisions are needed?
(d) With n = 5 compare the left endpoint approximation L_5, the right endpoint
approximation R_5 and their average to ln(2) (use a calculator.) Which is best?

2. In this problem we will see how to use Riemann Sums to calculate ln(2).
(a) According to the Fundamental Theorem of Calculus which bound b is needed to get
?1^b 1/x dx = ln(2)? Show your work.
(b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5
rectangles with equal bases. Is this an over or an under estimate?
(c) Give a clear explanation of how to estimate/calculate ln(2) to within an accuracy of ?,
for example, ? = 0.01. Specifically how many subdivisions are needed?
(d) With n = 5 compare the left endpoint approximation L5, the right endpoint
approximation R5 and their average to ln(2) (use a calculator.) Which is best?

Added by Isabel R.

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