MAT1320D Calculus 1
Assignment 1
Professor: José Malagón-López
Due 25 January, 2012
NAME:
STUDENT NUMBER:
• Read each question carefully, and answer all questions in the space provided after each question.
• The correct answers require justification written legibly and logically: you must convince the marker that
you know why your solution is correct. Simply writing the correct answer will earn you 0.
• All work handed in must be your own. Do not plagiarize.
• Staple all pages of your work together. If you do not do this and some pages are lost, you will not receive
credit for your work. It is not the marker’s job to track down missing pages.
• You may submit this assignment to me BEFORE CLASS, or by putting into the box marked “MAT1320
Section D” in the cabinet in the foyer of the math building (KED) on the due date, by 5pm.
FOR MARKER’s USE ONLY
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total
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2
p
ln(x) − 1.
[3]
1.
Find the domain, range and inverse function for y =
[4]
2.
Find the graph of the inverse function for the following graphs.
3
SHOW ALL YOUR WORK AND JUSTIFY YOUR ANSWERS!
[4]
3.
Find the values of C and a so that (0, 4) and (2, 1) are in the graph of an exponential function f (x) = Cax .
4.
Evaluate:
[2]
a) e3 ln(8)+ln(2)
[2]
b)
log3 (1) + log3 (2) − log3 (18).
4
SHOW ALL YOUR WORK AND JUSTIFY YOUR ANSWERS!
5.
Solve for x:
[3]
a)
42x−3 = 32x
[3]
b)
3 · 2x+1 = 7x+2
[3]
c)
ln x2 − 4x − 4 = 0
5
SHOW ALL YOUR WORK AND JUSTIFY YOUR ANSWERS!
d) ln x2 − x − 2 = 2 + ln(x + 1)
[3]
[4]
6.
Given f (x) = ln(x + 1) and g(x) =
√
x + 3, find an explicit formula of g ◦ f and (g ◦ f )−1 .
6
SHOW ALL YOUR WORK AND JUSTIFY YOUR ANSWERS!
[5]
7.
Solve cos2 (x) − 3 sin(x) = 3, for x on [0, 2π]. Hint: Obtain a quadratic equation for u = sin(x) and solve.
7
SHOW ALL YOUR WORK AND JUSTIFY YOUR ANSWERS!
8.
Find the exact value of
[2]
a)
arcsin(−1/2).
[2]
b)
√
arccos(− 3/2).