Questions from General Calculus


Q: Sketch the vector field F by drawing a diagram like Figure 5

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9. Figure 9: F (x, y) = y i + (x + y) j

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Q: If a is a constant vector, r = x i +

If a is a constant vector, r = x i + y j + z k, and S is an oriented, smooth surface with a simple, closed, smooth, positively oriented boundary curve C, show that

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Q: What is the connection between vector functions and space curves?

What is the connection between vector functions and space curves?

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Q: Find the gradient vector field of f. f (x

Find the gradient vector field of f. f (x, y) = y sin (xy)

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Q: Find the gradient vector field of f. f (s

Find the gradient vector field of f. f (s, t) = √ (2s + 3t)

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Q: Find the gradient vector field of f. f (x

Find the gradient vector field of f. f (x, y, z) = √ (x^2 + y^2 + z^2)

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Q: Find the gradient vector field of f. f (x

Find the gradient vector field of f. f (x, y, z) = x2yey/z

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Q: (a). What does it mean to say that f is

(a). What does it mean to say that f is continuous at (a, b)? (b). If f is continuous on R2, what can you say about its graph?

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Q: How do you find the tangent vector to a smooth curve at

How do you find the tangent vector to a smooth curve at a point? How do you find the tangent line? The unit tangent vector?

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Q: Write an expression for the area of a surface with equation z

Write an expression for the area of a surface with equation z = f (x, y), (x, y) ∈ D.

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