x xx - simulation

www.simulation-math.com
Introduction
Simulation programs and computational tools on www.simulation-math.com are designed to help students visualize
math concepts and gain deeper understanding of math concepts. Currently computational tools and graphing utilities
should be sufficient for students taking Elementary Statistics, College Algebra, Trigonometry, or Precalculus. It is our
hope that students enrolling in one of these courses who cannot afford a graphing calculator will take advantage of the
computational tools and graphing utilities available on www.simulation-math.com.
Simulation programs and computational tools for Calculus are being developed.
I. Simulation with Animated Charts
Simulation with Animated Charts
Template 1
Simulation of y = mx + b
Template 2
Simulation of y = a(x - h)2 + k
Template 3
Simulation of y = a(x - h)3 + k
Template 4
3
y

a

xh k
Simulation of
Template 5
Simulation of y = a|x - b| + c
Template 6
Simulation of Secant and Tangent Lines
Example 1
Template 7
Simulation of Tangent Lines
Example 1
Template 8
Use Newton's Method to approximate
the real solution(s) of
x3  2 x 2  x  4  0
.
Solution:
step 1:
Use general graphing utility to see where graph of f ( x)  x  2 x  x  4
3
2
crosses the x-axis.
Graph crosses x-axis between -6 and -2.
Step 2:
Use Simulation program for Newton's Method to approximate solution(s).
Approximate solution is:
-2.8454660914
Graph crosses x-axis between
-6 and -2.
Step 2:
Graph crosses x-axis between -4 and 0.
Use Simulation program for Newton's Method to approximate solution(s).
Approximate solution of x3  2 x2  x  4  0 is -4.15557379.
Template 9 Example 1
Mean Value Theorem
Let f ( x)  0.3x 2 + 0.3x  4. Show that f satisfies the hypotheses of the
Mean Value Theorem on the interval [-7, 2] and find all values c in this
interval whose existence is guaranteed by the Theorem.
Solution:
f ( x)  0.6 x+ 0.3.
Template 9 Example 2
Let f ( x)  x3 Show that f satisfies the hypotheses of the
Mean Value Theorem on the interval [-1, 2] and find all values c in this
interval whose existence is guaranteed by the Theorem.
Solution:
f ( x)  3x 2
Template 10
Normal Distribution: Fix μ and Vary σ
Template 11
Normal Distribution vs. Binomial Distribution
If n*p*(1 - p) ≥ 10, binomial random variable X is approximately normal
with mean of n*p and standard deviation of square root of [n*p*(1 - p)].
Template 12
Standard Normal Distribution vs. t-Distribution
Compare the standard normal distribution with a family of t-Distribution with the following
degrees of freedom: 1, 4, 8, 12, 25, 30, 40, 50, 60, 100