
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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When using Reimann sums, which approximation is the most accurate: left, right, or midpoint?
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- Use the given information to find the left and right- hand Riemann sums for the following function. If necessary, round your answers to five decimal places. ƒ(x) = x² a = -8, b Left-Hand Riemann Sum = = x² + 3 Right-Hand Riemann Sum = 4, and n = 7 OFarrow_forwardUse the function y=2x from x=0 to x=1 and n equal subintervals with the fuction evaluated at the left-hand endpoint of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). Then find a. S(10). b. S(100). c. S(1,000).arrow_forwardUse proof by contradiction to prove that if a and b are odd inte- gers, then 4 (a² +62).arrow_forward
- Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = cos 2x for 0, n= 40 a. Write the left Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.)arrow_forwardCompute the mid-point sum M4: use the function values at the midpoint of the each subinterval for the height of the rectangle. Shade the rectangles. 3 2 1 0 1/2 QA3 3/2 I Which one, L4, R4, or M4 is the best estimate of the area under the graph of f, above the x-axis and from x = 0 to x = 2? Why?arrow_forward
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