Exam Calculus 1
November 3, 2014: 9.0012.00.
This exam has 8 problems. Each problem is worth 1 point. Total: 8 + 1 (free) = 9 points;
more details can be found below. Write on each page your name and student number.
The use of annotations, books and calc
Homework 4 Calculus 1
The homework must be returned by Wednesday October 7, 1:00 pm.
1. The function f is given by
f (x) = e
1/x2
if x 6= 0 and f (0) = 0.
(a) Use the denition of derivative to compute f 0 (0).
(b) Is f 0 (x) dierentiable at x = 0?
2. The
Calculus 1 Homework 1 Solutions
September 12, 2015
1. The sequence a1 , a2 , a3 , . . . is dened by the recurrence relation
p
a1 = 1
an+1 = 6 + an n = 1, 2, 3, . . .
(a) Show (using the principle of mathematical induction) that the sequence is increasing,
Correctionmodel Homework 2 Calculus 1 20152016
Problem 1 (15 p)
Prove that if 1 is a natural number, then the 2nth derivative of
sin is given by (1) ( sin() 2 cos().
Use Mathematical induction:
Base step ( = 1):
2
( sin ) = sin + cos =>
( sin )
2
(sin
Homework 2 Calculus 1
The homework must be returned by September 21, 1:00 pm. It must be handed in the
mailbox associated with your tutorial group. The mailboxes are located next to the
reception desk in Nijenborgh 4.
1. Prove that if n
by
1 is a natural
Homework 3 Calculus 1
The homework must be returned by Tuesday September 29, 1:00 pm. It must be handed
in the mailbox associated with your tutorial group. The mailboxes are located next to
the reception desk in Nijenborgh 4.
1. Prove the following statem
Correction model Homework 3 calculus 1 20152016
Problem 1 (20p)
Prove the following statement using the precise definition of a limit:
sin
lim
=0
1 +
> 0 < => 

sin
0 <
1+
Correct definition 2p
sin
<
1+
sin  1
sin
1


<
1+
1+
1 +  >
1
Homework 1 Calculus 1
The homework must be returned by Monday September 14, 1:00 pm. It must be handed
in the mailbox associated with your tutorial group. The mailboxes are located near the
reception of Nijenborgh 4.
1. The sequence a1 , a2 , a3 , . is de
Homework 5 Calculus 1
The homework must be returned by Wednesday October 14, 1:00 pm. It must be handed
in the mailbox associated with your tutorial group.
1. The function f is given by
f (x) = e
1/x
als x 6= 0, en f (0) = p.
(a) Find the value(s) of p
Calculus I Homework 5 Grading Scheme
October 15, 2015
1
Question 1: 20 points
The function f is given by
f (x) = e
1/x
when x 6= 0 and f (0) = p.
(a) Find the value(s) of p that make(s) f continuous at 0? 4 pt
(b) For what value(s) of p is f dierentiabl
Calculus 1, Homework 4:
Solutions
Problem 1: 20p
Problem 1
The function f is given by
1
() =
2
If x =/= 0 and f(0)=0.
a. Use the definition of the derivative to compute f(0).
Solution:
Definition of the derivative is:
a: 12p
(+)()
0
() = lim
x, in this
Exam Calculus 1
23 october 2009, 13.0016.00.
This exam has 6 problems. The maximum score per problem can be found below. Write
on each page your name and student number, and on the first page your seminar group.
The use of annotations, books and calculat
Exam Calculus 1
October 30, 2015: 8.3011.30.
This exam has 8 problems. Each problem is worth 1 point. Total: 8 + 1 (free) = 9 points;
more details can be found below. Write on each page your name and student number.
The use of annotations, books and calc
Exam Calculus 1
4 february 2013, 9.0012.00.
This exam has 9 problems. Each problem is worth 1 point; more details can be found
below. Write on each page your name and student number, and on the first page your
seminar group. The use of annotations, books
Exam Calculus 1
5 november 2012, 14.0017.00.
This exam has 9 problems. Each problem is worth 1 point; more details can be found
below. Write on each page your name and student number, and on the first page your
seminar group. The use of annotations, book
Exam Calculus 1
November 4, 2013: 9.0012.00.
This exam has 8 problems. Each problem is worth 1 point. Total: 8 + 1 (free) = 9 points;
more details can be found below. Write on each page your name and student number.
The use of annotations, books and calc
Exam Calculus 1
7 november 2011, 14.0017.00.
This exam has 9 problems. Each problem is worth 1 point; more details can be found
below. Write on each page your name and student number, and on the first page your
seminar group. The use of annotations, book
Midterm Exam Calculus 1
28 September 2010. 9.0011.00.
Write on each page your name and student number, and on the first page your seminar
group. The use of annotations, books and calculators is not permitted in this examination. All answers must be suppo
Midterm Exam Calculus 1
23 september 2013, 9.0011.00.
Write on each page your name and student number, and on the first page your seminar
group. The use of annotations, books and calculators is not permitted in this examination. All answers must be suppo
Midterm Exam Calculus 1
26 September 2011, 9.0011.00.
Write on each page your name and student number, and on the first page your seminar
group. The use of annotations, books and calculators is not permitted in this examination. All answers must be suppo
Homework 6 Calculus 1
The homework must be returned by Friday October 24, 1:00 pm. It must be handed in
the mailbox associated with your tutorial group.
1. The factorial n! of a nonnegative integer n is the product of all positive integers less
than or e
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Midterm Exam Calculus 1
22 september 2014, 9.0011.00.
Write on each page your name and student number, and on the rst page your tutorial
group. The use of annotations, books and calculators is not permitted. All answers must
be supported by arguments/wor
Exam Calculus 1
November 4, 2013: 9.0012.00.
This exam has 8 problems. Each problem is worth 1 point. Total: 8 + 1 (free) = 9 points;
more details can be found below. Write on each page your name and student number.
The use of annotations, books and calc
Exam Calculus 1
8 february 2012, 9.0012.00.
This exam has 9 problems. Each problem is worth 1 point; more details can be found
below. Write on each page your name and student number, and on the rst page your
seminar group. The use of annotations, books a
Exam Calculus 1
4 february 2013, 9.0012.00.
This exam has 9 problems. Each problem is worth 1 point; more details can be found
below. Write on each page your name and student number, and on the rst page your
seminar group. The use of annotations, books a
Exam Calculus 1
December 2nd, 2013: 18:3021:30.
This exam has 8 problems. Each problem is worth 1 point. Total: 8 + 1 (free) = 9 points;
more details can be found below. Write on each page your name and student number.
The use of annotations, books and c