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 Equ
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 square
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)
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 th
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.
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
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:[email protected]
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 rela
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
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 coe
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 ri
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