Questions from Calculus

Q: Let / (a). Show that f

Let (a). Show that f (x, y) → 0 as (x, y) → (0, 0) along any path through s0, 0d of the form y = mxu with 0 (b). Despite part (a), show that f is discontinuous at...

Q: Show that the function f given by f (x) =

Show that the function f given by f (x) = |x | is continuous on Rn. [Hint: Consider |x - a |2 = (x – a) ∙ (x – a).]

Q: If c ∈ Vn, show that the function f given by

If c ∈ Vn, show that the function f given by f (x) = c ∙ x is continuous on Rn.

Q: Find the velocity, acceleration, and speed of a particle with

Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified value of t....

Q: Describe the level surfaces of the function. f (x

Describe the level surfaces of the function. f (x, y, z) = x2 - y2 - z2

Q: Describe how the graph of g is obtained from the graph of

Describe how the graph of g is obtained from the graph of f . (a). t (x, y) = f (x, y) + 2 (b). t (x, y) = 2f (x, y) (c). t (x, y) = -f (x, y) (d). t (x, y) = 2 - f (x, y)

Q: Describe how the graph of g is obtained from the graph of

Describe how the graph of g is obtained from the graph of f. (a). t (x, y) = f (x - 2, y) (b). t (x, y) = f (x, y + 2) (c). t (x, y) = f (x + 3, y – 4)

Q: Use a computer to graph the function using various domains and viewpoints

Use a computer to graph the function using various domains and viewpoints. Get a printout that gives a good view of the “peaks and valleys.” Would you say the function has a maximum value? Can you ide...

Q: Use a computer to graph the function using various domains and viewpoints

Use a computer to graph the function using various domains and viewpoints. Get a printout that gives a good view of the “peaks and valleys.” Would you say the function has a maximum value? Can you ide...

Q: Graph the function using various domains and viewpoints. Comment on the

Graph the function using various domains and viewpoints. Comment on the limiting behavior of the function. What happens as both x and y become large? What happens as (x, y) approaches the origin?