. Determine the value of a such that lim I--2 3x² + ax + a +3 x²+x-2 exists. Justify your answer.
. Determine the value of a such that lim I--2 3x² + ax + a +3 x²+x-2 exists. Justify your answer.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![1. Determine the value of a such that lim
3x² + ax + a +3
x²+x-2
I--2
Hint: Apply one of the Limit Laws.
1 1
2. Prove that lim = using the e-d-definition.
x 4 x
Hint: Consult the proof of lim
²: = 4 from Lecture 7. Assume [x - 4| < 1.
x→2
3. Consider the function
if x = Q
f(x) =
-r³ if x # Q.
Prove that f'(0) = 0.
Hint: Apply the conclusion in one of the problems in Problem Set 2.
4. A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket
price set at $12, average attendance at a game has been 11,000. A market survey indicates that
for each dollar the ticket price is lowered, average attendance will increase by 1000. How should
the owners of the team set the ticket price to maximize their revenue from ticket sales? Justify
your answer. (Let x denote the value of decrement in ticket price.)
5. Consider the function
f(x) =
if x = Q
if x # Q.
Show that f is not Riemann integrable on [0, 1].
n
Hint: Show that lim
f(x)^x does not exist. Recall that
can be any choice in [i-1,₁].
n→∞
6. A Tibetan monk leaves the monastery at 7:00am and takes his usual path to the top of the
mountain, arriving at 7:00pm. The following morning, he starts at 7:00am at the top and takes
the same path back, arrriving at the monastery at 7:00pm. Use the Intermediate Value Theorem
to show that there is a point on the path that the monk will cross at exactly the same time of
day on both days.¹
=
exists. Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3377bc7-6ef1-40f4-abe7-323568a857f3%2F748f7628-fee7-4009-b253-d9377a6e6e37%2Fggaazs6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Determine the value of a such that lim
3x² + ax + a +3
x²+x-2
I--2
Hint: Apply one of the Limit Laws.
1 1
2. Prove that lim = using the e-d-definition.
x 4 x
Hint: Consult the proof of lim
²: = 4 from Lecture 7. Assume [x - 4| < 1.
x→2
3. Consider the function
if x = Q
f(x) =
-r³ if x # Q.
Prove that f'(0) = 0.
Hint: Apply the conclusion in one of the problems in Problem Set 2.
4. A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket
price set at $12, average attendance at a game has been 11,000. A market survey indicates that
for each dollar the ticket price is lowered, average attendance will increase by 1000. How should
the owners of the team set the ticket price to maximize their revenue from ticket sales? Justify
your answer. (Let x denote the value of decrement in ticket price.)
5. Consider the function
f(x) =
if x = Q
if x # Q.
Show that f is not Riemann integrable on [0, 1].
n
Hint: Show that lim
f(x)^x does not exist. Recall that
can be any choice in [i-1,₁].
n→∞
6. A Tibetan monk leaves the monastery at 7:00am and takes his usual path to the top of the
mountain, arriving at 7:00pm. The following morning, he starts at 7:00am at the top and takes
the same path back, arrriving at the monastery at 7:00pm. Use the Intermediate Value Theorem
to show that there is a point on the path that the monk will cross at exactly the same time of
day on both days.¹
=
exists. Justify your answer.
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