Riemann Sum Grapher

Riemann Sum Grapher - This improved and expanded version of...

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* This improved and expanded version of the grapher is due to Jeff Morgan, Department of Mathematics, Tex This set of worksheets will automatically graph any function of x, show the (left) Riemann sum as a shaded ar Use the tabs at the bottom of the sheet to switch to the right sum grapher, or the midpoint sum grapher (whioc Instructions: Just enter the function in cell G13 (as shown; no equals sign) enter values for the limits of inte and a value between 1 and 200 for the number of partitions n. Notes: The number of partitions n cannot exceed 200 for this grapher Function: cos(3*x) Do not change the value of the Riemann Sum in cell I15. a: 0 The graph data is hidden on the right b: 1 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.3 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.6 0.63 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87 0.9 0.93 0.96 0.99 -1 -0.5 0 0.5 1 1.5
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Don’t touch this table!     x y u y_u 0.1 0 1 0 1 0.01 0.01 1 0 1 xas A&M University. 0.01 1 0 1 rea, and also ita value.  0.02 1 0 1 ch also shows the trapeziod sum). 0.02 1 0 1 0.03 1 0 1 egration a and b, 0.03 1 0 1 0.04 0.99 0 1 0.04 0.99 0 1 0.05 0.99 0 1 0.05 0.99 0 1 n: 10 0.06 0.99 0 1 0.06 0.98 0 1 0.07 0.98 0 1 0.07 0.98 0 1 0.08 0.97 0 1 0.08 0.97 0 1 0.09 0.97 0 1 0.09 0.96 0 1 0.1 0.96 0 1 0.1 0.96 0.1 0.96 0.11 0.95 0.1 0.96 0.11 0.95 0.1 0.96 Left Sum 0.12 0.94 0.1 0.96 0.15 0.12 0.94 0.1 0.96 0.13 0.93 0.1 0.96 0.13 0.92 0.1 0.96 pi 0.14 0.92 0.1 0.96 3.14 0.14 0.91 0.1 0.96 e 0.15 0.91 0.1 0.96 2.72 0.15 0.9 0.1 0.96 0.16 0.89 0.1 0.96 0.16 0.89 0.1 0.96 0.17 0.88 0.1 0.96 0.17 0.87 0.1 0.96 0.18 0.87 0.1 0.96 0.18 0.86 0.1 0.96 0.19 0.85 0.1 0.96 0.19 0.84 0.1 0.96 0.2 0.83 0.1 0.96 0.2 0.83 0.2 0.83 0.21 0.82 0.2 0.83 0.21 0.81 0.2 0.83 0.22 0.8 0.2 0.83 0.22 0.79 0.2 0.83 0.23 0.78 0.2 0.83 0.23 0.77 0.2 0.83 0.24 0.76 0.2 0.83 0.24 0.75 0.2 0.83 0.25 0.74 0.2 0.83 0.25 0.73 0.2 0.83 0.26 0.72 0.2 0.83 0.26 0.71 0.2 0.83 0.27 0.7 0.2 0.83
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0.27 0.69 0.2 0.83 0.28 0.68 0.2 0.83 0.28 0.67 0.2 0.83 0.29 0.66 0.2 0.83 0.29 0.64 0.2 0.83 0.3 0.63 0.2 0.83 0.3 0.62 0.3 0.62 0.31 0.61 0.3 0.62 0.31 0.6 0.3 0.62 0.32 0.59 0.3 0.62 0.32 0.57 0.3 0.62 0.33 0.56 0.3 0.62 0.33 0.55 0.3 0.62 0.34 0.54 0.3 0.62 0.34 0.52 0.3 0.62 0.35 0.51 0.3 0.62 0.35 0.5 0.3 0.62 0.36 0.48 0.3 0.62 0.36 0.47 0.3 0.62 0.37 0.46 0.3 0.62 0.37 0.44 0.3 0.62 0.38 0.43 0.3 0.62 0.38 0.42 0.3 0.62 0.39 0.4 0.3 0.62 0.39 0.39 0.3 0.62 0.4 0.38 0.3 0.62 0.4 0.36 0.4 0.36 0.41 0.35 0.4 0.36 0.41 0.33 0.4 0.36 0.42 0.32 0.4 0.36 0.42 0.31 0.4 0.36 0.43 0.29 0.4 0.36 0.43 0.28 0.4 0.36 0.44 0.26 0.4 0.36 0.44 0.25 0.4 0.36 0.45 0.23 0.4 0.36 0.45 0.22 0.4 0.36 0.46 0.2 0.4 0.36 0.46 0.19 0.4 0.36 0.47 0.17 0.4 0.36 0.47 0.16 0.4 0.36 0.48 0.15 0.4 0.36 0.48 0.13 0.4 0.36 0.49 0.12 0.4 0.36 0.49 0.1 0.4 0.36 0.5 0.09 0.4 0.36 0.5 0.07 0.5 0.07 0.51 0.06 0.5 0.07 0.51 0.04 0.5 0.07 0.52 0.03 0.5 0.07 0.52 0.01 0.5 0.07 0.53 0 0.5 0.07 0.53 -0.02 0.5 0.07 0.54 -0.03 0.5 0.07 0.54 -0.05 0.5 0.07 0.55 -0.06 0.5 0.07 0.55 -0.08 0.5 0.07 0.56 -0.09 0.5 0.07 0.56 -0.11 0.5 0.07
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0.57 -0.12 0.5 0.07 0.57 -0.14 0.5 0.07 0.58 -0.15 0.5 0.07 0.58 -0.17 0.5 0.07 0.59 -0.18 0.5 0.07 0.59 -0.2 0.5 0.07 0.6 -0.21 0.5 0.07 0.6 -0.23 0.6 -0.23 0.61 -0.24 0.6 -0.23 0.61 -0.26 0.6 -0.23 0.62 -0.27 0.6 -0.23 0.62 -0.29 0.6 -0.23 0.63 -0.3 0.6 -0.23 0.63 -0.31 0.6 -0.23 0.64 -0.33 0.6 -0.23 0.64 -0.34 0.6 -0.23 0.65 -0.36 0.6 -0.23 0.65 -0.37 0.6 -0.23 0.66 -0.38 0.6 -0.23 0.66 -0.4 0.6 -0.23 0.67 -0.41 0.6 -0.23 0.67 -0.43 0.6 -0.23 0.68 -0.44 0.6 -0.23 0.68 -0.45 0.6 -0.23 0.69 -0.47 0.6 -0.23 0.69 -0.48 0.6 -0.23 0.7 -0.49 0.6 -0.23 0.7 -0.5 0.7 -0.5 0.71 -0.52 0.7 -0.5 0.71 -0.53 0.7 -0.5 0.72 -0.54 0.7 -0.5 0.72 -0.56 0.7 -0.5 0.73 -0.57 0.7 -0.5 0.73 -0.58 0.7 -0.5 0.74 -0.59 0.7 -0.5 0.74 -0.6 0.7 -0.5 0.75 -0.62 0.7 -0.5 0.75 -0.63 0.7 -0.5 0.76 -0.64 0.7 -0.5 0.76 -0.65 0.7 -0.5 0.77 -0.66 0.7 -0.5 0.77 -0.67 0.7 -0.5 0.78 -0.68 0.7 -0.5 0.78 -0.7 0.7 -0.5 0.79 -0.71 0.7 -0.5 0.79 -0.72 0.7 -0.5 0.8 -0.73 0.7 -0.5 0.8 -0.74 0.8 -0.74 0.81 -0.75 0.8 -0.74 0.81 -0.76 0.8 -0.74 0.82 -0.77 0.8 -0.74 0.82 -0.78 0.8 -0.74 0.83 -0.79 0.8 -0.74 0.83 -0.8 0.8 -0.74 0.84 -0.8 0.8 -0.74 0.84 -0.81 0.8 -0.74 0.85 -0.82 0.8 -0.74 0.85 -0.83 0.8 -0.74 0.86 -0.84 0.8 -0.74
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0.86 -0.85 0.8 -0.74 0.87 -0.85 0.8 -0.74 0.87 -0.86 0.8 -0.74 0.88 -0.87 0.8 -0.74 0.88 -0.88 0.8 -0.74 0.89 -0.88 0.8 -0.74 0.89 -0.89 0.8 -0.74 0.9 -0.9 0.8 -0.74 0.9 -0.9 0.9 -0.9 0.91 -0.91 0.9 -0.9 0.91 -0.92 0.9 -0.9 0.92 -0.92 0.9 -0.9 0.92 -0.93 0.9 -0.9 0.93 -0.93 0.9 -0.9 0.93 -0.94 0.9 -0.9 0.94 -0.94 0.9 -0.9 0.94 -0.95 0.9 -0.9 0.95 -0.95 0.9 -0.9 0.95 -0.96 0.9 -0.9 0.96 -0.96 0.9 -0.9 0.96 -0.97 0.9 -0.9 0.97 -0.97 0.9 -0.9 0.97 -0.97 0.9 -0.9 0.98 -0.98 0.9 -0.9 0.98 -0.98 0.9 -0.9 0.99 -0.98 0.9 -0.9 0.99 -0.99 0.9 -0.9 1 -0.99 0.9 -0.9 1 -0.99 1 -0.9
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p q r s 0 0 1 1 1 0.1 0.96 0.96 2 0.2 0.83 0.83 3 0.3 0.62 0.62 4 0.4 0.36 0.36 5 0.5 0.07 0.07 6 0.6 -0.23 -0.23 7 0.7 -0.5 -0.5 8 0.8 -0.74 -0.74 9 0.9 -0.9 -0.9 10 1 -0.99 0 11 1.1 -0.99 0 12 1.2 -0.9 0 13 1.3 -0.73 0 14 1.4 -0.49 0 15 1.5 -0.21 0 16 1.6 0.09 0 17 1.7 0.38 0 18 1.8 0.63 0 19 1.9 0.83 0 20 2 0.96 0 21 2.1 1 0 22 2.2 0.95 0 23 2.3 0.82 0 24 2.4 0.61 0 25 2.5 0.35 0 26 2.6 0.05 0 27 2.7 -0.24 0 28 2.8 -0.52 0 29 2.9 -0.75 0 30 3 -0.91 0 31 3.1 -0.99 0 32 3.2 -0.98 0 33 3.3 -0.89 0 34 3.4 -0.71 0 35 3.5 -0.48 0 36 3.6 -0.19 0 37 3.7 0.1 0 38 3.8 0.39 0 39 3.9 0.65 0 40 4 0.84 0 41 4.1 0.96 0 42 4.2 1 0 43 4.3 0.94 0 44 4.4 0.81 0 45 4.5 0.59 0 46 4.6 0.33 0 47 4.7 0.04 0 48 4.8 -0.26 0 49 4.9 -0.53 0 50 5 -0.76 0 51 5.1 -0.92 0 52 5.2 -0.99 0 53 5.3 -0.98 0
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54 5.4 -0.88 0 55 5.5 -0.7 0 56 5.6 -0.46 0 57 5.7 -0.18 0 58 5.8 0.12 0 59 5.9 0.41
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