Answer to Question #72273 in Calculus for Lastone

Question

1. Use traces to sketch the graph of f(x, y) = p
16 − x
2 − 16y
2
.
2. For each of the following, identify the surface and sketch its graph.
a) x = 4y
2 + z
2 − 4z + 4.
b) x
2 + 4y
2 + z
2 − 2x = 0
3. a) What does the equation x
2 + y
2 = 1 represent as a curve in R
2
?
b) What does it represent as a surface in R
3
?
4. Find an equation of the tangent plane and normal to the surface at the specified point.
a) z = 4x
2 − y
2 + 2y; (−1, 2, 4)
b) z = y ln x; (1, 4, 0)
5. Find an equation for the tangent plane and find symmetric equations for the normal line
to the surface z = arctan( y
x
) at the point (1, 1,
Ï€
4
).
6. Sketch the region bounded above by the cone z =
p
x
2 + y
2 and below by the sphere
x
2 + y
2 + z
2 = z
7. Find the angle of inclination θ of the tangent plane to the surface 3x
2 + 2y
2 − z = 15 at
the point (2, 2, 5).

Answer 1

Dear Lastone, your question requires a lot of work, which neither of our experts is ready to perform for free. We advise you to convert it to a fully qualified order and we will try to help you. Please click the link below to proceed: Submit order