Questions from General Calculus


Q: Describe in words the region of R3 represented by the equation(

Describe in words the region of R3 represented by the equation(s) or inequality. x2 + y2 + z2 > 2z

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Q: Write inequalities to describe the region. The region between the

Write inequalities to describe the region. The region between the yz-plane and the vertical plane x = 5

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Q: Find the sum of the given vectors and illustrate geometrically.

Find the sum of the given vectors and illustrate geometrically. 3, −1 , −1, 5

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Q: Differentiate. f (t) = cot t / et

Differentiate. f (t) = cot t / et

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Q: Write inequalities to describe the region. The region consisting of

Write inequalities to describe the region. The region consisting of all points between (but not on) the spheres of radius r and R centered at the origin, where r < R

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Q: If A, B, and C are the vertices of a

If A, B, and C are the vertices of a triangle, find

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Q: Consider the points P such that the distance from P to A

Consider the points P such that the distance from P to A (-1, 5, 3d is twice the distance from P to B (6, 2, -2). Show that the set of all such points is a sphere, and find its center and radius.

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Q: Find an equation of the set of all points equidistant from the

Find an equation of the set of all points equidistant from the points A (-1, 5, 3) and B (6, 2, -2). Describe the set.

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Q: Find a + b, 4a + 2b, |a |,

Find a + b, 4a + 2b, |a |, and |a - b |. a = −3, 4 , b = 9, −1

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Q: What is the relationship between the point (4, 7)

What is the relationship between the point (4, 7) and the vector (4, 7)? Illustrate with a sketch.

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