1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).
1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).
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ISBN:9780470458365
Author:Erwin Kreyszig
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Math 292 – Test 3
Name:
Directions: YOU MUST SHOW ALL WORK TO RECEIVE CREDIT.
Giving a calculator answer with no additional work does not count as showing your work.
This test is open book and open notebook. All work must be completed on your own.
Discussing any portion of this test with another person is considered cheating on this test.
Sign on the line below to certify that you did not discuss this test with anyone and will not discuss the test
or share information about the test with anyone else on the test date, 12/2/2020.
Name:
Signature:
Note: If you are working on your own paper you are expected to include the above statement and
required signature on your paper at the start of the test.
Test Problems:
1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).
8z
2. Use the Chain Rule to find đu for z = (3x + cos 3y)5 with x = 1+ 3u and y = e2tu
3. a) Find the directional derivative of f(x, y) = Jxyz at the point (3, 2, 6) in the direction of
v = <-1,-2,2 >.
b) Give the maximum rate of change of f(x, y) = Jxyz at the point (3, 2, 6). In what direction does
this maximum occur?
4. a) Find all critical points of the function f(x, y) = e'(y² –x³)
b) Use the second derivatives test to determine if the function has a local maximum, local minimum,
or saddle point at each of these critical points.
5. Calculate the iterated integral: "y sin(xy)dxdy .
6. Calculate the volume of the solid that lies under the hyperbolic paraboloid x -3y +z=2 and above
the rectangle [-1,1]×[1,2].
Evaluate (f 2xydA where D is the triangular region with
0, 0), (1, 2), and (0, 3).
8. Sketch the region of integration and then give an equivalent double integral with the order of
integration reversed. CIS(x,y)dydx .
9. Evaluate the integral || e
* dA where D is the region to the left of the y-axis that lies between the
circles x + v? =1 and x+ v² =4.
10. Find the mass of a lamina that occupies the region bounded by 1- y and y = 0 if the lamina has
density function P(x,y) = kx for some nonzero constant k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8bbe1e1f-18dc-4f53-84a9-dc3dae6a4844%2F3e6989f5-731d-4660-a7c7-1bfb8f4c401d%2F6z00gkd_processed.png&w=3840&q=75)
Transcribed Image Text:l Boost LTE
8:07 AM
1 0 97%
moodle.mcneese.edu
Math 292 – Test 3
Name:
Directions: YOU MUST SHOW ALL WORK TO RECEIVE CREDIT.
Giving a calculator answer with no additional work does not count as showing your work.
This test is open book and open notebook. All work must be completed on your own.
Discussing any portion of this test with another person is considered cheating on this test.
Sign on the line below to certify that you did not discuss this test with anyone and will not discuss the test
or share information about the test with anyone else on the test date, 12/2/2020.
Name:
Signature:
Note: If you are working on your own paper you are expected to include the above statement and
required signature on your paper at the start of the test.
Test Problems:
1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).
8z
2. Use the Chain Rule to find đu for z = (3x + cos 3y)5 with x = 1+ 3u and y = e2tu
3. a) Find the directional derivative of f(x, y) = Jxyz at the point (3, 2, 6) in the direction of
v = <-1,-2,2 >.
b) Give the maximum rate of change of f(x, y) = Jxyz at the point (3, 2, 6). In what direction does
this maximum occur?
4. a) Find all critical points of the function f(x, y) = e'(y² –x³)
b) Use the second derivatives test to determine if the function has a local maximum, local minimum,
or saddle point at each of these critical points.
5. Calculate the iterated integral: "y sin(xy)dxdy .
6. Calculate the volume of the solid that lies under the hyperbolic paraboloid x -3y +z=2 and above
the rectangle [-1,1]×[1,2].
Evaluate (f 2xydA where D is the triangular region with
0, 0), (1, 2), and (0, 3).
8. Sketch the region of integration and then give an equivalent double integral with the order of
integration reversed. CIS(x,y)dydx .
9. Evaluate the integral || e
* dA where D is the region to the left of the y-axis that lies between the
circles x + v? =1 and x+ v² =4.
10. Find the mass of a lamina that occupies the region bounded by 1- y and y = 0 if the lamina has
density function P(x,y) = kx for some nonzero constant k.
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