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Lesson: Left Endpoint Riemann Sum

Worksheet • 8 Questions

Q1:

The table shows the values of a function obtained from an experiment. Estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with left endpoints.

π‘₯ 5 7 9 11 13 15 17
𝑓 ( π‘₯ ) βˆ’ 3 βˆ’ 1 . 7 βˆ’ 0 . 6 0.4 1.8 2.5 3.1

Q2:

Given that 𝑓 ( π‘₯ ) = 4 π‘₯ c o s and that 0 ≀ π‘₯ ≀ πœ‹ 4 , evaluate, to the nearest six decimal places, the Riemann sum for 𝑓 with six subintervals, taking the sample points to be left endpoints.

Q3:

Given that 𝑓 ( π‘₯ ) = π‘₯ c o s and that 0 ≀ π‘₯ ≀ 4 πœ‹ 3 , evaluate, to the nearest six decimal places, the Riemann sum for 𝑓 with six subintervals, taking the sample points to be left endpoints.

Q4:

Given that 𝑓 ( π‘₯ ) = 4 π‘₯ c o s and that 0 ≀ π‘₯ ≀ 3 πœ‹ 5 , evaluate, to the nearest six decimal places, the Riemann sum for 𝑓 with six subintervals, taking the sample points to be left endpoints.

Q5:

Given that 𝑓 ( π‘₯ ) = π‘₯ c o s and that 0 ≀ π‘₯ ≀ πœ‹ 2 , evaluate, to the nearest six decimal places, the Riemann sum for 𝑓 with six subintervals, taking the sample points to be left endpoints.

Q6:

The table shows the values of a function obtained from an experiment. Estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with left endpoints.

π‘₯ 2 6 10 14 18 22 26
𝑓 ( π‘₯ ) βˆ’ 3 . 8 βˆ’ 2 . 8 βˆ’ 1 . 6 βˆ’ 0 . 7 βˆ’ 0 . 2 0.6 1.7

Q7:

The table shows the values of a function obtained from an experiment. Estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with left endpoints.

π‘₯ 3 7 11 15 19 23 27
𝑓 ( π‘₯ ) βˆ’ 3 . 3 βˆ’ 2 . 4 βˆ’ 1 . 7 βˆ’ 0 . 4 0.8 1.7 2.2

Q8:

The table shows the values of a function obtained from an experiment. Estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯   οŠͺ d using three equal subintervals with left endpoints.

π‘₯ 4 5 6 7 8 9 10
𝑓 ( π‘₯ ) βˆ’ 2 . 9 βˆ’ 2 βˆ’ 0 . 9 0.1 1.5 2.4 3.1
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