5. Any line in R^3 is determined by an equation of the form ax + by + cz = d Tru

Question

5. Any line in R^3 is determined by an equation of the form ax + by + cz = d

True or False

6. Suppose f(x) is a continuous function of one real variable. Define F(x) = integral from x to 0 f(y)dy. The fundamental theorem of calculus states in part that

a. the derivative of F with respect to x is f

b. the derivative of f with respect to x is F

7. You are riding home from class on a skateboard and want to figure out how far your journey is, taking into account the precise path you travel (including turns, hills, and vert tricks). What technique is most appropriate for this calculation?

a.Integration of vector-valued functions

b.Differentiation of vector-valued functions

c.Double integration in polar coordinates.

d. Taking the cross product of the curvature and integrating.

Explanation / Answer

Answer :

5. False.

In an x-y-z Cartesian coordinate system the general form of the equation of a plane is ax + by + cz + d = 0 .

6. Suppose f(x) is a continuous function of one real variable. Define F(x) = integral from x to 0 f(y)dy. The fundamental theorem of calculus states in part states that the derivative of F with respect to x is f.

7..The best technique is Integration of vector-valued functions

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