MA101 Week 2 Report - Review of Dierentiaion
Name:
Student Number:
Lab
Winter 2014
1. [6 marks] Find the derivatives of each of the following functions. Simplify your results as much as possible.
(a) u(t) = (2t)3t
2
+1
(b) f (x) = sin(cos(tan x)
ln(u(t) =
MA101 Week 3 Report - IVT; MVT
Name:
Student Number:
1. [4 marks] Let f (x) = 6 7x2 , x > 0. Find
d 1
f (x)
dx
Lab
Winter 2014
d 1
1
2 . Hint: use the formula dx f (x) = f [f 1 (x)] .
x=
3
Method 1:
to use the formula, we need to nd f 1 (2/3). This means
MA101 Week 4 Report - The Squeeze Theorem; LHspitals Rule
o
Name:
Student Number:
Lab
Winter 2014
. Notice that lim g(x) cannot be evaluated by direct
x0
x
substitution or by using basic algebra. Dene g in Maple by entering:
g:=(x)->sqrt(x3+x2) * sin (Pi/
MA101 Week 5 Report - Antiderivatives, FTOC, Integration
Name:
Student Number:
Lab
Winter 2014
1. [8 marks] Evaluate the following limits. Indicate all indeterminate forms encountered and the points at which
LHospitals rule is applied. Justify your answer
MA101 Week 6 Report - Applications of Integration; Substitution
Name:
Student Number:
Lab
Winter 2014
2
xe13x dx.
1. [5 marks] Consider the integral w =
(a) Load the student package in Maple and dene the above integral as follows:
with(student):
w:=Int(x*
MA101 Week 8 Report - Integration By Parts
Name:
Student Number:
Lab
Winter 2014
1. [3 marks] Suppose g(x) is a continuous function whose derivative g (x) is also continuous, with g(3) = 0 and
g(5) = ln 6. Use the substitution rule to evaluate
5
g (x)eg(x
MA101 Week 12 Report - Dierential Equations; Separable Equations
Name:
Student Number:
Lab
Winter 2014
1. [5 marks] Find a formula for the curve y = f (x) given that its slope at the point (x, y) is e ln y2y cos(3x + 1)
Find the general solution that dene
MA101 Mock Final Exam
Name:
Time Allowed: 150 minutes
Total Value: 80 marks
Number of Pages: 8
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while completing the mock test. Please note, that the cheat s
MA100 Lab Notes
Text References: SZ: 1.5, 1.6, 6.1
Review last weeks lab notes regarding symmetry, domains and ranges of functions. This week in the labs we will be
considering arithmetic of functions and how that affects domains and ranges.
We will also
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MA100 Lab Report 3 - Functions Continued
Name:
Student Number:
1. [3 marks] Consider the function s(t) =
Fall 2016
t + 2 + 4. Determine the difference quotient and simplify your results.
t + h + 2 + 4 (
MA101 Lab 3 Notes
The Squeeze Theorem (Sandwich Theorem)
If g (x) f (x) h (x) for all x in an open interval containing a [ except possibly at a itself ],
and lim g (x) = lim h (x) = L, then lim f (x) = L.
x!a
x!a
(OR if g (x)
x!a
f (x)
h (x) for all x "ne
MA101 Lab 2 Notes
Derivatives of:
1. Trigonometric Functions:
d
sin x = cos x
dx
d
csc x = csc x cot x
dx
Note: By the Chain Rule,
d
cos x = sin x
dx
d
sec x = sec x tan x
dx
d
tan x = sec2 x
dx
d
cot x = csc2 x
dx
d
(sin(f (x) = cos(f (x) f 0 (x); etc.
d
MA101 Lab Report 5
Page 1
MA101 Lab Report 5 Notes
Linear Approximations (Last Weeks Lab)
A function f can be approximated by the tangent line (or linear) approximation of f at x = a which
is given by:
L(x) = f (a) + f 0 (a)(x
a)
A common misconception is
MA101 Lab Report 4
Page 1
MA101 Lab Report 4 Notes
Indeterminate Forms and LHospitals Rule
If lim
x!a
g(x)
0
results in an indeterminate form of or
f (x)
0
g(x)
g 0 (x)
= lim 0
:
x!a f (x)
x!a f (x)
1
, then LHospitals Rule states that:
1
lim
Other indete
MA101 Lab Report 1 Notes
Basic Rules of Dierentiation
Constant Function Rule:
d
[k] = 0, k 2 R
dx
Constant Multiple Rule:
d
[k f (x)] = k f 0 (x), k 2 R
dx
Sum/Dierence Rule:
d
= [f (x)
dx
g (x)] = f 0 (x)
g 0 (x)
d n
[x ] = nxn 1 , n 2 R
dx
Power Rule:
P
MA101 Lab Report 1
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Name:
YES or NO
Winter 2017
1. [4 marks] Find the indicated derivative for each of the following functions.
(a)
dy
when y = tan(x + sin x)
dx
(b)
dy
= sec2 (x + sin x)(1 + cos x)
dx
MA101 Lab Report 3
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Student Number:
Name:
1. [3 marks] Consider f (x) = sec x and g(x) =
(a) Plot f (x);
YES or NO
Winter 2017
sin x
:
x
1
; and g(x) for x 2 [ 1; 1] in Maple.
f (x)
f:=(x)->sec(x); g:=(x)->sin(x)/x; p
MA101 Lab Report 2
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Winter 2017
1. [6 marks] Recall Question #5 from Lab Report 1 where a mass m (in gm) oscillated vertically with simple harmonic motion
and s(t) represented the displ
MA101 Lab Report 5
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Name:
1. [8 marks] Consider the function f (x) = 3 ln(1
YES or NO
Winter 2017
x).
(a) Determine each of the following.
f (x) = 3 ln(1
1
f 0 (x) = 3
f 00 (x) =
f 000 (x) =
x)
1
0
x
(
MA101 Lab Report 4
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Student Number:
Name:
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Winter 2017
1. [7 marks] Evaluate each of the following limits using LHospitals Rule.
(a)
lim+
1
ln t
t
lim
1
ln t
t
t!1
t!1+
= lim
t!1+
1
1
ln t + (t
lim (cos x + x
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MA100 Lab Report 3 - Functions Continued
Name:
Student Number:
1. [3 marks] Consider the function s(t) =
s(t + h)
h
p
t + 2 + 4. Determine the dierence quotient and simplify your results.
p
p
t + h + 2 +