University of Guelph - TT4
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School
University of Guelph *
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Course
1200
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
3
Uploaded by ChancellorToadPerson676
Online Homework System Assignment Worksheet 11/6/20 - 1:20:25 PM EST
Name:
____________________________ Class:
Calculus 1 - MATH*1200 - F20
Class #:
____________________________ Section #:
____________________________ Instructor:
Mihai Nica
Assignment:
Term Test #4
Question 1: (0 points)
Fill in your name on the academic integrity pledge:
"As a member of the University of Guelph, I pledge to uphold the highest standards of ethics and academic integrity. This means that I will only use my notes, a calculator, and will NOT use any other outside assistance
(no internet
or other people
including my peers). I understand that there are serious consequences
, including getting expelled from the course or the university, for violating academic integrity." Write the phrase "I, --insert name here--, agree to the academic integrity pledge" on your first page.
Reminder:
-It is helpful to your grader to copy out any equations in your question in your answer -Dont forget to save a copy of your questions (e.g. by hitting print -> save as pdf, or by taking a screenshot) to submit Q0 [1pt]
Which notation do you like better: dydx
or y′
?
Give a one sentence explanation of why you like it better. Q1 [3pt] Consider the function h(x)={14x14x2if x<0if x≥0
Use the limit definition
of the derivative to evaluate h′(0)
. (Hint: Which tool from the limits warchest is useful for doing the limits of piecewise functions?) Q2 On the domain x>0
, let h(x)=x5ln(3x)
. Q2a) [1pt]
A student is trying to the derivative of this function and gets the answer: h′(x)=(5ln(3x))x5ln(3x)−1
. This is not correct. Explain to the student why this is not correct, and be sure to explicitly call out which derivative rule(s) were not used correctly. Q2b) [2pt]
Using the methods we did in the course, find the derivative h′(x)
correctly. (Grading Hint: You do NOT need to simplify your answer) Q3 [4pt] Find the second derivative d2ydx2
at the point (x,y)=(6,0)
where x
and y
satisfy e7y+7y=6x−35
(Hint: Don't forget chain rule!)
Q4 To celebrate being half done the term, Professor Nica is making a drawing of Pretzel's the dog wearing a party hat in Desmos which looks like this: The picture is made of mathematically defined curves. The face of the dog is a blue oval whose equation is 1618x2+918y2
=
16
The party hat is a green triangle. The sloped sides are tangent to the oval and touch the oval at the points (3,4)
and (−3,4)
. The tip of the party hat is on the y-axis. Q4a) [2pt]
Using the given information, find the slope of the side of the party hat that goes through (3,4)
. Q4b) [1pt]
Using the given information and the answer from part a), find how tall
is the party hat (This height is labelled as "party hat height" in the diagram). Q5 [6pt]
Diana is launching a hot air balloon. The hot air balloon is attached to a spool of rope on the ground. When the ballon is on the ground, the spool is 8 meters away from the balloon. The hot air balloon rises vertically straight up into the air in such a way that the length of rope from the spool to the balloon is increasing at a rate of 3 meters per second. What is the vertical velocity of the hot air balloon at the moment when the hot air balloon is 3 meters off the ground? In your solution, be clear on what is the variable, what are the functions, and what is the relationship between the functions you are using.
A diagram of the hot air balloon when it is on the ground and again after it has been released into the air.
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