Questions from General Calculus


Q: Which of the following four planes are parallel? Are any of

Which of the following four planes are parallel? Are any of them identical?

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Q: Which of the following four lines are parallel? Are any of

Which of the following four lines are parallel? Are any of them identical?

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Q: Find the distance between the given parallel planes. 6z =

Find the distance between the given parallel planes. 6z = 4y - 2x, 9z = 1 - 3x + 6y

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Q: Show that the distance between the parallel planes ax + by

Show that the distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is //

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Q: Find equations of the planes that are parallel to the plane x

Find equations of the planes that are parallel to the plane x + 2y - 2z = 1 and two units away from it.

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Q: Where does the normal line to the parabola y = x2 -

Where does the normal line to the parabola y = x2 - 1 at the point (-1,0) intersect the parabola a second time? Illustrate with a sketch.

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Q: Show that the lines with symmetric equations x = y = z

Show that the lines with symmetric equations x = y = z and x + 1 = y/2 = z/3 are skew, and find the distance between these lines.

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Q: Differentiate the function. f (x) = sin(

Differentiate the function. f (x) = sin(ln x)

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Q: Find the distance between the skew lines with parametric equations x =

Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t, and x = 1 + 2s, y = 5 + 15s, z = -2 + 6s.

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Q: Determine whether each statement is true or false in R3.

Determine whether each statement is true or false in R3. (a). Two lines parallel to a third line are parallel. (b). Two lines perpendicular to a third line are parallel. (c). Two planes parallel to a...

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