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Q: Find the average value of the function on the given interval.

Find the average value of the function on the given interval.

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Q: Find the average value of the function on the given interval.

Find the average value of the function on the given interval.

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Q: The table shows values of a force function f(x)

The table shows values of a force function f(x) where x is measured in meters and f(x) in newtons. Use the Midpoint Rule to estimate the work done by the force in moving an object from x = 4 to x = 20...

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Q: The figure shows a horizontal line y = c intersecting the curve

The figure shows a horizontal line y = c intersecting the curve y = 8x - 27x3. Find the number c such that the areas of the shaded regions are equal.

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Q: There is a line through the origin that divides the region bounded

There is a line through the origin that divides the region bounded by the parabola y = x - x2 and the x-axis into two regions with equal area. What is the slope of that line?

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Q: (a) Find a positive continuous function f such that the

(a) Find a positive continuous function f such that the area under the graph off from 0 to t is A(t) = t3 for all t. 0. (b) A solid is generated by rotating about the x-axis the region under the curv...

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Q: If the tangent at a point P on the curve y =

If the tangent at a point P on the curve y = x3 intersects the curve again at Q, let A be the area of the region bounded by the curve and the line segment PQ. Let B be the area of the region defined i...

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Q: Suppose we are planning to make a taco from a round tortilla

Suppose we are planning to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill...

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Q: Sketch the region enclosed by the given curves and find its area

Sketch the region enclosed by the given curves and find its area.

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Q: Suppose the graph of a cubic polynomial intersects the parabola y =

Suppose the graph of a cubic polynomial intersects the parabola y = x2 when x = 0, x = a, and x = b, where 0 < a < b. If the two regions between the curves have the same area, how is b related to a?

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