Questions from General Calculus


Q: If a0 + a1 + a2 + ∙∙∙ + ak = 0

If a0 + a1 + a2 + ∙∙∙ + ak = 0, show that If you don’t see how to prove this, try the problem-solving strategy of using analogy...

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Q: Find the interval of convergence of /

Find the interval of convergence of /

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Q: Suppose you have a large supply of books, all the same

Suppose you have a large supply of books, all the same size, and you stack them at the edge of a table, with each book extending farther beyond the edge of the table than the one beneath it. Show that...

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Q: Find the sum of the series /

Find the sum of the series /

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Q: If p > 1, evaluate the expression /

If p > 1, evaluate the expression

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Q: Suppose that circles of equal diameter are packed tightly in n rows

Suppose that circles of equal diameter are packed tightly in n rows inside an equilateral triangle. (The figure illustrates the case n = 4.) If A is the area of the triangle and An is the total area o...

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Q: A sequence {an} is defined recursively by the equations

A sequence {an} is defined recursively by the equations Find the sum of the series /

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Q: If the curve y = e-x/10 sin x

If the curve y = e-x/10 sin x, x ≥ 0 is rotated about the x-axis, the resulting solid looks like an infinite decreasing string of beads. (a) Find the exact volume of the nth bead. (Use either a table...

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Q: Starting with the vertices P1(0, 1), P2(

Starting with the vertices P1(0, 1), P2(1, 1), P3(1, 0), P4(0, 0) of a square, we construct further points as shown in the figure: P5 is the midpoint of P1P2, P6 is the midpoint of P2P3, P7 is the mid...

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Q: Find the sum of the series /

Find the sum of the series /

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