Questions from General Calculus


Q: Find the minimum value of the area of the region under the

Find the minimum value of the area of the region under the curve y = x + 1/x from x = a to x = a + 1.5, for all a > 0.

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Q: Find the area under the curve y = 1/x3 from

Find the area under the curve y = 1/x3 from x = 1 to x = t and evaluate it for t = 10, 100, and 1000. Then find the total area under this curve for x > 1.

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Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

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Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

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Q: Sketch the region and find its area (if the area is

Sketch the region and find its area (if the area is finite).

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Q: If the units for are feet and the units for a (

If the units for are feet and the units for a (x) are pounds per foot, what are the units for da/dx? What units does f82 a(x) dx have?

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Q: Sketch the region and find its area (if the area is

Sketch the region and find its area (if the area is finite).

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Q: (a). Graph the functions f (x) = 1

(a). Graph the functions f (x) = 1/x1.1 and g (x) = 1/x0.9 in the viewing rectangles [0, 10] by [0, 1] and [0, 100] by [0, 1]. (b). Find the areas under the graphs of f and g from x = 1 to x = t and e...

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Q: Show that ½ (Tn + Mn) = T2n.

Show that ½ (Tn + Mn) = T2n.

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Q: Determine whether each integral is convergent or divergent. Evaluate those that

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

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