Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Question
Please answer (8c), thanks!
![forward or backward? Is it going faster or slowing down?
c) When does the mass stop?
8 cm
b) v(t) = 8 cos(t), a(t) = -8 sin(t): c) s) = cm, v=7a)
v(n) = -8, a(n) = Omoving backward and constant velocity; d) t = ! п 3п
6x²-10
x-x3x²+4x
g) lim
7. Find the indicated limits, use +∞ or -∞ when appropriate. Use L'Hospital's rule when needed (be sure to justify
why you can use it)
x-4
a) lim
x4r_16
a) 1/8
b) 3√2
b) lim
x
Cos x-1
x-0 x
h)lim
3
cos t
c) 16/5
c) lim
x-5
d)
i) lim
3x²-14x-5
x2-5x
sin 4x
x-0 x
sin x
x→∞ ex
j) lim
g) 2; h) 0; i) 4
d) lim
x→0
2 sec (approximately 1.5 sec, 4.7 sec, 7.8 sec, ...)
8 cm
j) 0
moving forward, slowing down and S(T) = 0,
3x²-14x-5
x2−5x
k) lim
In x
e) lim
x-0+ ex-1
5√√x-1
x--∞ 10x²-x
1) lim
In x
X→∞ X
k) 0 1) 0 m) ∞
f) lim tanh x
x→−8
m) lim e¹x
x→0+
8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts,
asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points
b) r(x) = x² - 4x³ + 1 c) f (x) = xe-x
In x
a) f(x) =
9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizi
function, determine the domain of the optimizing function, check the second derivative for optimum value, and write t
answer in complete sentence including appropriate units
a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with
largest possible volume. Determine the maximum volume.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2Fac4ab090-0c24-4b79-99b6-ef203e96c5ef%2Fx6h9n6i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:forward or backward? Is it going faster or slowing down?
c) When does the mass stop?
8 cm
b) v(t) = 8 cos(t), a(t) = -8 sin(t): c) s) = cm, v=7a)
v(n) = -8, a(n) = Omoving backward and constant velocity; d) t = ! п 3п
6x²-10
x-x3x²+4x
g) lim
7. Find the indicated limits, use +∞ or -∞ when appropriate. Use L'Hospital's rule when needed (be sure to justify
why you can use it)
x-4
a) lim
x4r_16
a) 1/8
b) 3√2
b) lim
x
Cos x-1
x-0 x
h)lim
3
cos t
c) 16/5
c) lim
x-5
d)
i) lim
3x²-14x-5
x2-5x
sin 4x
x-0 x
sin x
x→∞ ex
j) lim
g) 2; h) 0; i) 4
d) lim
x→0
2 sec (approximately 1.5 sec, 4.7 sec, 7.8 sec, ...)
8 cm
j) 0
moving forward, slowing down and S(T) = 0,
3x²-14x-5
x2−5x
k) lim
In x
e) lim
x-0+ ex-1
5√√x-1
x--∞ 10x²-x
1) lim
In x
X→∞ X
k) 0 1) 0 m) ∞
f) lim tanh x
x→−8
m) lim e¹x
x→0+
8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts,
asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points
b) r(x) = x² - 4x³ + 1 c) f (x) = xe-x
In x
a) f(x) =
9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizi
function, determine the domain of the optimizing function, check the second derivative for optimum value, and write t
answer in complete sentence including appropriate units
a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with
largest possible volume. Determine the maximum volume.
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