Bobo reached the maximum
height at 19.7m at 1.8 seconds
,koo
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16
z
1.74
Seconds
Amount of time Bobo was
more than 16.0m above the
ground.
This is where Bobo hits the
Point where Bobo
was fired in the
Solutions to Practice Questions for Test1
a) [ y 1 , y 2 , y 3 ,
I.
b) [ x 3 , x 5 ,
c) [ x 2 ,
y2 + y +1
]
y2
x2
]
x+3
1
]
2
a) [ 4( x 2 y )(3 x y ) ]
II.
b) [ 2b 2 (a 2)(a 2 + 2a + 4) ]
2
y 3 y 3y 9
+ 2 ]
c) [ x 2 +
2 z 4 2z z
6
3
2 1
1
d) [ 1
a)
MOUNT ROYAL COLLEGE
Department of Mathematics, Physics and Engineering
MATH 0131 Calculus
SAMPLE FINAL EXAMINATION 1
TOTAL MARKS: 100
TOTAL TIME: 2 hours
Please show your work in the space provided.
NO CALCULATORS ARE ALLOWED.
MARKS:
(14) 1. Let f ( x)
5
1) Solve this differential equation to show that the velocity
*
At t=0,
V(t)=(v0 +
2) show that the height of the ball. Until it hits the ground.
V(t)=(v0 +
V(t)=(v0 +
(0) = 0 =
C=
3) Let t1 be the time that the ball takes to reach its maximum height.
)
)
Math 0131
SOLUTIONS TO PRACTICE PROBLEMS FOR TEST 1 (FUNCTIONS)
y
In this case, m = -2 and the change in x or x = 3 .
x
y
So 2 =
and y = 6 In other words, when x increases by 3, y decreases by 6.
3
b) The average rate of change of y with respect to x for
SOLUTION TO REVIEW PROBLEMS FOR TEST # 2
1. Find the instantaneous rate of change of f(x) =
Using the limit definition,
2. Let f(x) =
1
1 x
df
dx
f 1 (5)
x
5
2
1 x
with respect to x at x = 5 . (Chapter 5)
1
8
3. Find the equation of the tangent line to
1
PRACTICE PROBLEMS FOR TEST # 3
Differentiation of Exponential, and Logarithmic Functions
Know the Differentiation Formulas for Exponential and Log functions:
1
1
(log b x)
(ln x )
(b x )b x ln b
(e x )e x
x ln b
x
1. Find derivatives of the following fu
Polynomial Functions Project
1. Y= P(x)
Explanation: You know that y is less than zero so it would start at the bottom.
You also know x is greater than 3 so you got your first x intercept. Next y is
greater than zero so it would start at the top. You also
Below is the exam. To clarify, chose any two of the four
options.
Answer any two of the following four essay questions:
1). Choose at least three readings from the textbook and discuss how they have
advanced your thinking about deviance.
2). You have been