Questions from General Calculus


Q: Verify the given linear approximation at a = 0. Then determine

Verify the given linear approximation at a = 0. Then determine the values of for which the linear approximation is accurate to within 0.1. tan x ≈ x

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Q: Verify the given linear approximation at a = 0. Then determine

Verify the given linear approximation at a = 0. Then determine the values of for which the linear approximation is accurate to within 0.1. 1/ (1 + 2x)4 ≈ 1 - 8x

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Q: Verify the given linear approximation at a = 0. Then determine

Verify the given linear approximation at a = 0. Then determine the values of for which the linear approximation is accurate to within 0.1. ex ≈ 1 + x

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Q: Use a linear approximation (or differentials) to estimate the given

Use a linear approximation (or differentials) to estimate the given number. (2.001)5

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Q: Differentiate the function. H (z) = ln √

Differentiate the function. H (z) = ln √a2 – z2/a2 + z2

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Q: Use a linear approximation (or differentials) to estimate the given

Use a linear approximation (or differentials) to estimate the given number. (8.06)2/3

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Q: If a tank holds 5000 gallons of water, which drains from

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after minutes a...

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Q: Explain, in terms of linear approximations or differentials, why the

Explain, in terms of linear approximations or differentials, why the approximation is reasonable. sec 0.08 ≈ 1

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Q: If c > 1/2, how many lines through the

If c > 1/2, how many lines through the point (0, c) are normal lines to the parabola y = x2? What if c < 1/2?

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Q: Explain, in terms of linear approximations or differentials, why the

Explain, in terms of linear approximations or differentials, why the approximation is reasonable. (1.01)6 ≈ 1.06

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