Bobo reached the maximum
height at 19.7m at 1.8 seconds
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16
z
1.74
Seconds
Amount of time Bobo was
more than 16.0m above the
ground.
This i
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
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.
N
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 ti
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)
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 . (Chap
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
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
g
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
a