MAT 137Y: Calculus!
Problem Set 9 Solutions
Due in tutorial on March 10-11
Total: 22 points.
1. [7 points.]
N
Find and prove a closed formula for
i=1
1
.
i(i + 1)
First, we compute the sum for a few values of N to try to guess the pattern:
1
1
=
12
2
1
1
MAT 137Y: Calculus!
Problem Set 8 Solutions
Due in tutorial on February 24-25
Total: 19 points
1. [0 points]
The average is
18
0+1+3+3+71+5
=
7
7
2. [0 points]
Here is the graph of g :
7
6
5
4
3
2
1
1
2
3
4
5
We can break the domain into ve subintervals o
MAT 137Y: Calculus!
Problem Set 10 Solutions
Due in tutorial on March 31-April 1
Total: 29 points.
1. (a) [2 points.]
Find two series
an and
n=1
bn such that:
n=1
an is divergent,
n=1
bn is divergent, and
n=1
(an + bn ) is convergent.
n=1
One easy example
MAT 137Y: Calculus!
Problem Set 4 Solutions
Due in tutorial on November 4-5
Total: 33 points.
1. [4 points.]
We know the following data about the function f :
x
0
f (x)
1
f (x)
2
f (x)
3
We dene a new function by g(x) = f (xf (x). Compute g (0).
g (x) = f
MAT 137Y: Calculus!
Problem Set 5 Solutions
Due in tutorial on November 18-19
Total: 40 points.
1. [12 points; 3 points per part.]
Compute the derivatives of the following functions. Simplify your answers as
much as possible, and box your nal answers.
(a)
MAT 137Y: Calculus!
Problem Set 3. Solutions
Due in tutorial on October 2728
1. [9 points, 3 points per part.]
Compute the derivatives of the following functions.
(a) f (x) = sin2 x + sin(x2 ) + sin(2x) + (sin 2)x + 2 sin x
f (x) = 2 sin x cos x + 2x cos(