Questions from Calculus

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?

Q: Investigate the family of functions f (x, y) =

Investigate the family of functions f (x, y) = ecx2+y2. How does the shape of the graph depend on c?

Q: Use a computer to investigate the family of surfaces z

Use a computer to investigate the family of surfaces z = (ax2 + by2) e-x2-y2 How does the shape of the graph depend on the numbers a and b?

Q: Use a computer to investigate the family of surfaces z = x2

Use a computer to investigate the family of surfaces z = x2 + y2 + cxy. In particular, you should determine the transitional values of c for which the surface changes from one type of quadric surface...

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: Graph the functions / In general, if

Graph the functions In general, if t is a function of one variable, how is the graph of obtained from the graph of t?

Q: Suppose that lim (x, y) → (3,

Suppose that lim (x, y) → (3, 1) f (x, y) = 6. What can you say about the value of f (3, 1)? What if f is continuous?

Q: Explain why each function is continuous or discontinuous. (a

Explain why each function is continuous or discontinuous. (a). The outdoor temperature as a function of longitude, latitude, and time (b). Elevation (height above sea level) as a function of longitude...

Q: Use a table of numerical values of f (x, y

Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as (x, y) → (0, 0). Then explain why your guess i...

Q: Use a table of numerical values of f (x, y

Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as (x, y) → (0, 0). Then explain why your guess i...