Attached, you will find three copies of the graph of f(x)=√4-(x − 3)². 1. Goal: approximate the area under the curve usi

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Attached You Will Find Three Copies Of The Graph Of F X 4 X 3 1 Goal Approximate The Area Under The Curve Usi 1 (59.6 KiB) Viewed 7 times

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Attached, you will find three copies of the graph of f(x)=√4-(x − 3)². 1. Goal: approximate the area under the curve using four rectangles, using the right hand side of the rectangle to find the height. (i) Sketch the four rectangles you will use on your graph. (Graphs provided on last page) (ii) On your graph, x1 = x2 = x3 = X4 = (ii) Height of rectangle 1 Height of rectangle 2 Height of rectangle 3 Height of rectangle 4 = f(x₁) ~ = f(x₂) ~ = f(x3) ~ = f(x4) ~ (iii) The width of each rectangle is Ax =
(iv) ⇒ Area of rectangle 1 Area of rectangle 2 Area of rectangle 3 (v) = f(x₁) Ax≈ = f(x₂)Ax~ = f(x3)Ax~ Area of rectangle 4 = f(x4) Ax≈ ~ ⇒ Total approximate area = 22 22 Σf(x₁) Ax i=1 + + +
2. Goal: Approximate the area under the curve using 16 rectangles and right-hand Rie- mann sums, using # 1 as a guide.
3. Imagine doing this with 1000 rectangles. Draw "1000" rectangles on a graph. What do you notice?
4. Using geometry, find the exact area under the curve.
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