Math 117 Practice Midterm 3
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final solution. Show your work.
Problem 1
Solve the differential Equation
xy' - 2x = x2
y(1) = 5
Solution
Solve for y':
xy'
The Least Squares Regression Line
Example:
Suppose you have three points in the plane and want to find the line
y = mx + b
that is closest to the points. Then we want to minimize the sum of the squares of the vertical
distances, that is find m and b such
Math 117 Practice Midterm I
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final answer. Show your work.
Problem 1
Let
f(x,y) = xy - ln(2x - y)
Find
A.
Solution
We treat y as the variable and x as a
Math 117 Practice Midterm 2
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final answer. Show your work.
Problem 1
The following table gives the probability distribution for the number of kittens in
Partial Derivatives
Definition of a Partial Derivative
Let f(x,y) be a function of two variables. Then we define the partial derivatives as
Definition of the Partial Derivative
if these limits exist.
Algebraically, we can think of the partial derivative o
Practice Final
Please work out each of the problems below. Credit will be based on the steps towards the
final answer. Show your work.
Problem 1
Sketch the following.
A. The point (3,4,1).
Solution
We draw the xyz-axes, the shadow at the point (3,4) in th
MATH 117
CALCULUS for SOCIAL AND LIFE SCIENCES
Tuesday and Thursday 8:00 to 9:50 AM
Room A 211
4 UNITS
Instructor: Larry Green
Phone Number
Office: 541-4660 Extension 341
Internet e-mail:.greenl@ltcc.edu
Home Page: http:/www.ltcc.edu/academics.asp?scatID=
Locating and Classifying Local Extrema
Definition of Relative Max and Min
We now extend the definition of relative max and min to functions of two variables.
Definition
1. A function f(x,y) has a relative maximum at (a,b) if there is a
small circle center
Lagrange Multipliers
Lagrange Multipliers
Suppose that we have a function f(x,y) that we want to maximize in the restricted domain g(x,y)
= c for some constant c. Then we can look at the level curves of f and seek the largest level
curve that intersects t
Surfaces
Planes
Just as lines are the simplest and most important curves, planes are the most important surfaces.
The general plane has equation
ax + by + cz = d
To graph a plane with all positive coefficients, we just plot the three points where the plan
3 Dimensional Coordinates
Definitions
To generalize the plane to 3 dimensions, we draw a third axis, called the z-axis at a right angle
from the plane so that if you grab on to the z-axis with your right hand your hand will curl from
the positive x-axis t
Functions of Several Variables
Definition of Functions of Several Variables
A function of several variables is a function where the domain is a subset of Rn and range is R.
Example:
f(x,y) = x - y
is a function of two variables
g(x,y,z) = (x - y)/(y - z)