Questions from Calculus


Q: Determine all Taylor polynomials for f (x) = x2 +

Determine all Taylor polynomials for f (x) = x2 + 2x + 1 at x = 0.

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Q: A patient receives M mg of a certain drug daily. Each

A patient receives M mg of a certain drug daily. Each day, the body eliminates a fraction q of the amount of the drug present in the system. After extended treatment, estimate the total amount of the...

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Q: The infinite series a1 + a2 + a3 + … has partial

The infinite series a1 + a2 + a3 + … has partial sums given by Sn = 3 – 5/n. (a) Find ∑k=1 10 ak. (b) Does the infinite series converge? If so, to what value does it converge?

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Q: The infinite series a1 + a2 + a3 + … has partial

The infinite series a1 + a2 + a3 + … has partial sums given by Sn = n – 1/n. (a) Find ∑k=110 ak. (b) Does the infinite series converge? If so, to what value does it converge?

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Q: Determine the sums of the following infinite series: ∑k

Determine the sums of the following infinite series: ∑k=0 ∞ (5/6)k

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Q: Determine the sums of the following infinite series: ∑k

Determine the sums of the following infinite series: ∑k=0 ∞ (7/10)k

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Q: Determine the sums of the following infinite series: ∑j

Determine the sums of the following infinite series: ∑j=1 ∞ 5-2j

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Q: Determine the sums of the following infinite series: ∑j

Determine the sums of the following infinite series: ∑j=0 ∞ (-1)j/3j

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Q: Determine the sums of the following infinite series: ∑k

Determine the sums of the following infinite series: ∑k=0 ∞ (-1)k 3k+1/5k

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Q: Determine the sums of the following infinite series: ∑k

Determine the sums of the following infinite series: ∑k=1 ∞ (1/3)2k

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