Questions from General Calculus


Q: Determine whether the series converges or diverges. /

Determine whether the series converges or diverges.

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Q: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

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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: Match the differential equation with its direction field (labeled I–

Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.

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Q: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

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Q: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

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Q: Experiment with values of k between 3.4 and 3.

Experiment with values of k between 3.4 and 3.5. What happens to the terms?

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Q: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

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Q: The meaning of the decimal representation of a number 0.d1d2d3

The meaning of the decimal representation of a number 0.d1d2d3 ... (where the digit di is one of the numbers 0, 1, 2, . . . , 9) is that Show that this series always converges.

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Q: (a) Show that the function defined by /

(a) Show that the function defined by is not equal to its Maclaurin series. (b) Graph the function in part (a) and comment on its behavior near the origin.

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