WebAssign
15.2 (Homework)
Current Score : 1 / 107
Khaled Omar
MAT 211, section TTH Sp19 15409, Spring 2019
Instructor: Jay Abramson
Due : Tuesday, January 29, 2019 11:59 PM MSTLast Saved : n/a Saving... ()
1. –/4 pointsWaneFMAC7 15.2.002.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
UNDEFINED.)
, and
(1, −1)
f(x, y) = 1,500 + 5x − 2y
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
(1, −1)
(1, −1)
=
=
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
2. –/4 pointsWaneFMAC7 15.2.003.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
UNDEFINED.)
, and
(1, −1)
f(x, y) = 5x2 − y3 + x − 2
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
(1, −1)
(1, −1)
=
=
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
3. –/4 pointsWaneFMAC7 15.2.007.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
UNDEFINED.)
f(x, y) = 6x2y
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
(1, −1)
(1, −1)
=
=
, and
(1, −1)
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
4. –/4 pointsWaneFMAC7 15.2.010.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
UNDEFINED.)
, and
(1, −1)
f(x, y) = x−5y2 + xy2 + 5xy
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
(1, −1)
(1, −1)
=
=
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
5. –/4 pointsWaneFMAC7 15.2.012.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
, and
(1, −1)
UNDEFINED.)
f(x, y) =
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
=
(1, −1)
=
(1, −1)
2
(xy + 1)1
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
6. –/4 pointsWaneFMAC7 15.2.018.
Calculate
∂f , ∂f , ∂f
∂x ∂y ∂x
, and
(1, −1)
UNDEFINED.)
f(x, y) = 8xe5xy
∂f
=
∂x
∂f
=
∂y
∂f
∂x
∂f
∂y
=
(1, −1)
=
(1, −1)
∂f
∂y
when defined. (If an answer is undefined, enter
(1, −1)
7. –/8 pointsWaneFMAC7 15.2.020.
Find
∂2f , ∂2f , ∂2f , and ∂2f .
∂y∂x
∂x2 ∂y2 ∂x∂y
f(x, y) = 1,000 + 4x − 6y
∂2f
=
∂x2
∂2f
=
∂y2
∂2f =
∂x∂y
∂2f =
∂y∂x
Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂2f (1, −1)
=
∂x2
∂2f (1, −1)
=
∂y2
∂2f (1, −1) =
∂x∂y
∂2f (1, −1) =
∂y∂x
8. –/8 pointsWaneFMAC7 15.2.023.
Find
∂2f , ∂2f , ∂2f , and ∂2f .
∂y∂x
∂x2 ∂y2 ∂x∂y
f(x, y) = 2x2y
∂2f
=
∂x2
∂2f
=
∂y2
∂2f =
∂x∂y
∂2f =
∂y∂x
Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂2f (1, −1)
=
∂x2
∂2f (1, −1)
=
∂y2
∂2f (1, −1) =
∂x∂y
∂2f (1, −1) =
∂y∂x
9. –/8 pointsWaneFMAC7 15.2.026.
Find
∂2f , ∂2f , ∂2f , and ∂2f .
∂y∂x
∂x2 ∂y2 ∂x∂y
f(x, y) = e2x + y
∂2f =
∂x2
∂2f
=
∂y2
∂2f =
∂x∂y
∂2f =
∂y∂x
Evaluate them all at (1, −1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂2f (1, −1)
=
∂x2
∂2f (1, −1)
=
∂y2
∂2f (1, −1) =
∂x∂y
∂2f (1, −1) =
∂y∂x
10.–/6 pointsWaneFMAC7 15.2.032.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) =
32
x2 + y2 + z2
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
11.–/6 pointsWaneFMAC7 15.2.034.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) = 8xyez + 9xeyz + exyz
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
12.–/6 pointsWaneFMAC7 15.2.036.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) = 6x0.1y0.9 + z2
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
13.–/6 pointsWaneFMAC7 15.2.037.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) = 21exyz
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
14.–/6 pointsWaneFMAC7 15.2.039.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) =
4,000z
1 + y0.8
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
15.–/6 pointsWaneFMAC7 15.2.040.
Find
∂f , ∂f , and ∂f . HINT [See Example 3.]
∂x ∂y
∂z
f(x, y, z) =
e0.5x
1 + e−0.2y
∂f
=
∂x
∂f
=
∂y
∂f
=
∂z
Find their values at (0, −1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)
∂f (0, −1, 1)
=
∂x
∂f (0, −1, 1)
=
∂y
∂f (0, −1, 1)
=
∂z
16.–/9 pointsWaneFMAC7 15.2.060.
A production formula for a student's performance on a difficult English examination is given by
g(t, x) = 4tx − 0.2t2 − x2,
where g is the grade the student can expect to get, t is the number of hours of study for the
examination, and x is the student's grade-point average.
(a) Calculate gt(10, 3) and gx(10, 3).
gt(10, 3) =
gx(10, 3) =
Interpret the results.
If you have studied for
hours and have a GPA of
the examination is increasing by
and by
(b) What does the ratio
, your score on
points for each additional hour of study
points for each additional point of GPA.
gt(10, 3)
tell about the relative merits of study and grade-point
gx(10, 3)
average?
At a level of
hours of study with a GPA of
of study is equivalent to an increase of
GPA (as far as your test score is concerned).
, one additional hour
(rounded to three decimal places) in
17.1/14 points | Previous AnswersWaneFMAC7 15.2.064.
Recall that the compound interest formula for continuous compounding is
A(P, r, t) = Pert
where A is the future value of an investment of P dollars after t years at an interest rate of r.
(a) Calculate
∂A , ∂A , and ∂A , all evaluated at (90, 0.1, 10). (Round your answers to two
∂P ∂r
∂t
decimal places.).
∂A
=
∂P
∂A
=
∂r
∂A
=
∂t
Interpret your answers.
For a $
investment at
% interest invested for
years
and compounded continuously, the accumulated amount is increasing at a rate of $
per $1 of principal, at a rate of $
rate of $
per increase of 1 in r, and at a
per year.
(b) What does the function
∂A
∂P
of t tell about your investment?
(90, 0.1, t)
AP(90, 0.1, t) tells you the rate at which the accumulated amount in an account bearing
% interest, compounded continuously, with a principal of $
growing per $1
---Select---
after the investment.
in the
principal
,
, is
years
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