Questions from General Calculus


Q: A hawk flying at 15 m/s at an altitude of

A hawk flying at 15 m/s at an altitude of 180 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation until it hits the ground, where y is its height a...

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Q: The Gateway Arch in St. Louis (see the photo on

The Gateway Arch in St. Louis (see the photo on page 543) was constructed using the equation for the central curve of the arch, where x and y are measured in meters and |x|

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Q: Find a power series representation for the function and determine the interval

Find a power series representation for the function and determine the interval of convergence.

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Q: (a) The figure shows a telephone wire hanging between two

(a) The figure shows a telephone wire hanging between two poles at x 2b and x b. It takes the shape of a catenary with equation y c + a cosh (x/a). Find the length of the wire. (b) Suppose two telepho...

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Q: Find the length of the curve /

Find the length of the curve

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Q: The curves with equations xn + yn = 1, n =

The curves with equations xn + yn = 1, n = 4, 6, 8, . . . , are called fat circles. Graph the curves with n = 2, 4, 6, 8, and 10 to see why. Set up an integral for the length L2k of the fat circle wi...

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Q: Explain why each of the following integrals is improper. /

Explain why each of the following integrals is improper.

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Q: Which of the following integrals are improper? Why? /

Which of the following integrals are improper? Why?

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Q: Find the area under the curve y = 1/x3 from

Find the area under the curve y = 1/x3 from x = 1 to x = t and evaluate it for t = 10, 100, and 1000. Then find the total area under this curve for x > 1.

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Q: (a) Graph the functions f(x) = 1

(a) Graph the functions f(x) = 1/x1.1 and t(x) = 1/x0.9 in the viewing rectangles [0, 10] by [0, 1] and [0, 100] by [0, 1]. (b) Find the areas under the graphs of f and t from x = 1 to x = t and evalu...

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