Questions from General Calculus


Q: Determine whether the series is convergent or divergent by expressing sn as

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. If it is convergent, find its sum.

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Q: Determine whether the sequence converges or diverges. If it converges,

Determine whether the sequence converges or diverges. If it converges, find the limit.

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Q: (a) The curve y = x2, 0 < x

(a) The curve y = x2, 0 < x < 1, is rotated about the y-axis. Find the area of the resulting surface. (b) Find the area of the surface obtained by rotating the curve in part (a) about the x-axis.

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Q: Use series to evaluate the limit. /

Use series to evaluate the limit.

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Q: Use Simpson’s Rule with n = 10 to estimate the area of

Use Simpson’s Rule with n = 10 to estimate the area of the surface obtained by rotating the sine curve in Exercise 7 about the x-axis. Data from Exercise 7: Use Simpson’s Rule with n = 10 to estimat...

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Q: Determine whether the series is absolutely convergent or conditionally convergent.

Determine whether the series is absolutely convergent or conditionally convergent.

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Q: Find the length of the curve /

Find the length of the curve

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Q: (a) A direction field for the differential equation y’ =

(a) A direction field for the differential equation y’ = y(y-2) (y-4) is shown. Sketch the graphs of the solutions that satisfy the given initial conditions. (b) If the initial condi...

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Q: Solve the initial-value problem. /

Solve the initial-value problem.

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Q: Solve the initial-value problem. /

Solve the initial-value problem.

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