Questions from General Calculus


Q: Some laser printers use Bézier curves to represent letters and other symbols

Some laser printers use Bézier curves to represent letters and other symbols. Experiment with control points until you find a Bézier curve that gives a reasonable representation of the letter C.

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Q: More complicated shapes can be represented by piecing together two or more

More complicated shapes can be represented by piecing together two or more Bézier curves. Suppose the first Bézier curve has control points P0, P1, P2, P3 and the second one has control points P3, P4,...

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Q: In view of the answers to Problems 4 and 5, how

In view of the answers to Problems 4 and 5, how do you explain the results of Problems 1 and 2? Data from Problems 1: Use your computer algebra system to evaluate f(x) for x = 1, 0.1, 0.01, 0.001, a...

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Q: Use your computer algebra system to evaluate f(x) for

Use your computer algebra system to evaluate f(x) for x = 1, 0.1, 0.01, 0.001, and 0.0001. Does it appear that f has a limit as x→ 0?

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Q: Use the CAS to graph f near x = 0. Does

Use the CAS to graph f near x = 0. Does it appear that f has a limit as x→ 0?

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Q: Show that any tangent line to a hyperbola touches the hyperbola halfway

Show that any tangent line to a hyperbola touches the hyperbola halfway between the points of intersection of the tangent and the asymptotes.

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Q: Determine whether the series is absolutely convergent or conditionally convergent.

Determine whether the series is absolutely convergent or conditionally convergent.

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Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

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Q: Calculate the volume generated by rotating the region bounded by the curves

Calculate the volume generated by rotating the region bounded by the curves y = ln x, y = 0, and x = 2 about each axis. (a) The y­ axis (b) The x­ axis

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Q: Evaluate the integral. /

Evaluate the integral.

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