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Stewart_Calc_7ET ch14sec03
MULTIPLE CHOICE
1. Find for .
a.
b.
c.
d.
e.
0
2. Find for the function .
a.
b.
c.
d.
e.
3. How many nth-order partial derivatives does a function of two variables have?
a.
b.
c.
d.
e.
4. Use the definition of partial derivatives as limits to find if
.
a.
b.
c.
d.
e.
5. Find the indicated partial derivative.
a.
b.
c.
d.
e.
6. Find the indicated partial derivative.
a.
b.
c.
d.
e.
7. Use implicit differentiation to find
a.
b.
c.
d.
8. Use implicit differentiation to find
a.
b.
c.
d.
9. Find for the function
a.
b.
c.
d.
10. Find for the function
a.
b.
c.
d.
11. The height of a hill (in feet) is given by
where x is the distance (in miles) east and y is the distance (in miles) north of your cabin. If
you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of
change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?
a.
(a) 570 ft/mi, (b) 690 ft/mi
b.
(a) –570 ft/mi, (b) 690 ft/mi
c.
(a) 690 ft/mi, (b) 570 ft/mi
d.
(a) 690 ft/mi, (b) –570 ft/mi
12. The ellipsoid intersects the plane in an ellipse. Find parametric
equations for the tangent line to this ellipse at the point (1, 2, 2).
a.
b.
c.
d.
e.
13. If R is the total resistance of three resistors, connected in parallel, with resistances
, then
.
If the resistances are measured in ohms as , with a
possible error of 0.8% in each case, estimate the maximum error in the calculated value of
R.
a.
0.347
b.
0.476
c.
0.291
d.
0.098
e.
0.957
NUMERIC RESPONSE
1. Find all the second partial derivatives.
2. Find .
3. The ellipsoid intersects the plane in an ellipse. Find parametric
equations for the tangent line to this ellipse at the point (1, 2, 2).
4. Find the first partial derivatives of the function.
5. Find the differential of the function.
6. Find for .
7. Find for .
8. Find all the second partial derivatives of
9. Find for the function .
1. Find the first partial derivatives of the function .
2. Find the first partial derivatives of the function
3. Find the second partial derivatives of the function
4. Find the first partial derivatives of the function
5. Find the first partial derivatives of the function .
6. Use partial derivatives to find the implicit derivative
7. Use partial derivatives to find the implicit partial derivatives and
