MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 9
Fridays questions
Determine whether the following sequences are convergent or divergent. If theyre convergent, nd their limit.
cfw_
n
1.
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 3
Mondays questions
Find the derivative of the following functions.
y
1. g(y) = 2 t2 sin tdt
Solution: g (y) = y 2 sin y
2. g(x) =
1/x
0
ar
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 6
Mondays questions
1.
23
3
x
dx
16x2
0
Solution: x = 4 sin ,
2.
a
0
0
3
x
dx
16x2
=
40
3
x2 a2 x2 dx
Solution: x = a sin ,
3.
23
a
0
x2
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 2
Mondays questions
Find the area under the following curves as a limit of sums. Do not evaluate.
1. f (x) = x for 0 x 3.
Solution: limn
n
3
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 4
Mondays questions
Find the area bounded by the following curves.
1. y = x2 and y = 4x x2 .
Solution:
2. (*) y =
2
0
[(4x x2 ) x2 ]dx =
x,
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 10
Wednesdays questions
Determine whether the following sequences converge or diverge. If the converge, determine
their limit.
1. cfw_arctan
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 8
Mondays questions
Sketch the direction elds for the following equations.
1. y = 1 + y
Solution:
10
y(t)
K
4
5
K
0
2
2
4
t
K
5
K
10
2. y =
MAT136H1F Calculus I (B)
Fall 2012, Challenge problems Week 7
Wednesdays questions
Determine if the following are convergent or divergent, and evaluate them if convergent.
1
1.
dx
(3x + 1)2
1
Soluti