San Jos City College
Mathematics 72
Practice Exercises for the Final Examination
1. Determine whether the series
9! 3 k 2
8+ k2
k =5
2. Determine whether the series
1
sin n
n =1
3. Determine whether the series
4. Let
a1 = 1
n =1
converges or diverges.
San Jos City College
Mathematics 72
Practice Exercises for the Final Examination
1. Determine whether the series
9! 3 k 2
8+ k2
k =5
2. Determine whether the series
1
sin n
n =1
3. Determine whether the series
4. Let
a1 = 1
n =1
converges or diverges.
San Jos City College
Mathematics 72
Practice Quiz 2 (Sections 6.1 - 6.5)
1. Find an exact value of the length of the curve given by f ( x ) = 2 x
3
2
from x = 0 to x = 3 .
2. Set up a definite integral which is equal to the area bounded by the curves y =
San Jos City College
Mathematics 72
Practice Test 1 (Chapter 5)
2 x4
1. If g ( x) =
et sin(t ) dt , find g ( x ) .
3
0
z
1
2. Find the value (in exact form) of the following definite integral :
2
1
dx .
1 x2
0
3. Find the midpoint and trapezoidal rule app
Strategy for Integration
As we have seen, integration is more challenging than differentiation. In nding the derivative of a function it is obvious which differentiation formula we should apply. But it may
not be obvious which technique we should use to i
Strategy for Integration
As we have seen, integration is more challenging than differentiation. In nding the derivative of a function it is obvious which differentiation formula we should apply. But it may
not be obvious which technique we should use to i
Linear Differential Equations
A rst-order linear differential equation is one that can be put into the form
dy
dx
1
Pxy
Qx
where P and Q are continuous functions on a given interval. This type of equation occurs
frequently in various sciences, as we will