Questions from General Calculus


Q: The resistivity of a conducting wire is the reciprocal of the conductivity

The resistivity of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters (Ωm). The resistivity of a given metal depends on the temperature...

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Q: Use a Maclaurin series in Table 1 to obtain the Maclaurin series

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

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Q: Use a Maclaurin series in Table 1 to obtain the Maclaurin series

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

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Q: Find the area of the region enclosed by one loop of the

Find the area of the region enclosed by one loop of the curve.

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Q: Use a Maclaurin series in Table 1 to obtain the Maclaurin series

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

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Q: Find the Maclaurin series of f (by any method) and

Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these p...

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Q: Let fn(x) = (sin nx)/n2.

Let fn(x) = (sin nx)/n2. Show that the series ∑fn(x) converges for all values of x but the series of derivatives ∑fn'(x) diverges when x = 2nπ, an integer. For what values of x does the series ∑fn"(x)...

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Q: If the radius of convergence of the power series ∑∞n=

If the radius of convergence of the power series ∑∞n=0cnxn is 10, what is the radius of convergence of the series ∑∞n=0ncnxn-1? Why?

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Q: Find the Maclaurin series of f (by any method) and

Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these p...

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Q: Use the Maclaurin series for ex to calculate e-0.

Use the Maclaurin series for ex to calculate e-0.2 correct to five decimal places.

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