Chapter 2 Limits and Continuity
Exercise 1
1. Evaluate each of the following limits.
2.
1
3.
4.
2
5.
6.
3
7.
4
Chapter 4 Differentiating
&
Chapter 5 Advanced topics in differentiation
5
19.
20.Computing the derivative of the following functions.
6
7
8
9
10
Find the first two derivatives of each of the following functions
11
12
Chapter 6 Applications of the derivatives
13
Chapter 7 Integration
&
Chapter 9 Applications of integration
14
15
16
17
Evaluating the indefinite integral of the following functions.
18
19
20
21
22
23
24
25
26
27
Chapter 10 Differential Equations
1.If the differential equation is given as
,
rewrite it in the form
,
where
2.
Find the integrating factor
28
.
3.
Evaluate the integral
4.
Write down the general solution
.
5.
If you are given an IVP, use the initial condition to find the constant C.
6.Consider the autonomous equation
with parameter a.
(1). Draw the bifurcation diagram for this differential equation.
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(2).Find the bifurcation values and describe how the behavior of the solutions changes close to each bifurcation value.
7. Solve the equation
knowing that y1 = 2 is a particular solution.
8. Find all the solutions of
9. Find all the solutions to
10. Consider the autonomous differential equation with the initial condition
.
(1).Find .
(2).Find the first five terms of the Euler Approximation when .
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(3).Is there a contradiction between the results of 1 and 2 ? If yes, explain what happened.
11. Find the approximated sequence , for the IVP
.
12. Find the solution of
13.Let be the solution to the IVP
and be the solution to the IVP
Find the Wronskian of
. Deduce the general solution to
14.Find the general solution to the Legendre equation
,
31
using the fact that is a solution.
15. Find the solution to the IVP
16. Find a particular solution to the equation
17. Find the particular solution to
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