MONTGOMERY COLLEGE ROCKVILLE - Department of Mathematics
MA 110 Finite Mathematics Fall 2017
CRN 24859 ONLINE
Instructor: Atul N Roy
Office: SC254 P Rockville
Fridays: 10:30-12:30 PM
Fragmentos tomados de:
Escndalo de corrupcin sacude a la FIFA. EN: Semana.com
Los cargos que la Justicia de EE. UU. presenta contra los dirigentes del ftbol mundial giran en
torno a la "corrupcin generalizada durante las dos ltimas dcadas", en
Math 280 Review Problems
1. Find the equation for the plane that contains the point P(2,1,1) and also contains the line with
parametric equations x = 1 + 3t, y = 2t , z = 2 t.
2. Find an equation for the plane that contains the points P(3,2,-1), Q(4,1,1),
Quiz 6 solutions
1. Use Lagrange multipliers to maximize f(x, y) 4 x 2 y 2 subject to the constraint 2x + y = 1.
We need to solve f g .
f 2x,2y , g 2,1
2x + y = 1
Then x , y , substitute into the constraint to get 2 1
In single-variable calculus, we have functions of one independent variable. We are familiar with
graphs, derivatives, and integrals of such functions. In multivariable calculus, we look at
functions of several variables, that is, more
Test 1 solutions
(Homework problems similar to the test problems are noted.)
a 1,1,2 and b 2,1,3 (See 9.2 and 9.3, esp. 9.3 #15, 25, and quiz 1)
Find the following:
a) a b = (1)(2) + 1(1) + 2(3) = 5
b) a vector of length 2 in the opp
There are several ways to define a surface.
As the graph of a function z = f(x, y): We have already seen that the graph of a function of two
independent variables is a surface in 3. For example, the graph of f(x, y) = 6 3x 2y is a
During this course we will look at a variety of different types of functions. They differ not only
in the number of variables, but also in what the domain and range consist of.
We are very familiar with functions of a single variable, also ca
Now back to functions of several variables. We already looked briefly at functions of 2 variables
in section 9.6. In this section we will add to that, and also expand what we have done to
functions of more than two independent variables.
Previously, we have usually used functions of only one independent variable, but there are many
familiar examples of functions of two independent variables.
The temperature at a particular moment of a location on earth depends on the location,
As you know, when we have functions of a single variable that are composite functions, we need
to use the chain rule to find the derivative. If y f x and x gt then the composite function
is y f gt and the derivative of the composite can be fo