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Chain Rule Practice Problems
Chain Rule Practice Problems
The following will require more than one application of the Chain Rule:
Chain Rule Practice Problems
The following three problems require a more formal use of the chain rule.
9.3 Slope Fields PRACTICE
Match the slope field to its differential equation
All windows are
-3<x<3 and -3<y<3
dy
I.
= yx
dx
dy
II.
= 4 y(1 y)
dx
2
y
dy
III.
= e 4 sin( y)
dx
dy
IV.
= y(1+ x)
dx
Hint: find when dy/dx
is 0 or undefined first.
Steps to dr
9.4 Logistic Growth
Columbian Ground Squirrel
Glacier National Park, Montana
Photo by Vickie Kelly, 2004
Greg Kelly, Hanford High School, Richland, Washington
Weve used the exponential growth equation y = y0 e
to represent population growth.
kt
The expone
5.6: u Substitution
5.6: u Substitution
Evaluate:
(2x + 2)e
x 2 +2 x+3
dx
This seems rather difficult, but we can make it a ton easier.
Let u = x + 2x + 3
2
The inside function of the exponential
du
Then
= 2x + 2 du = (2x + 2)dx
dx
5.6: u Substitution
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differentiate (A*cos(wt+f) in relation to t
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9.3 Day 2: Euler s Method
Leonhard Euler was a Swiss
mathematician who made huge
contributions to mathematics,
almost half after he was totally
blind.
(When this portrait was made
he had already lost most of
the sight in his right eye.)
Leonhard Euler 170
AP Calculus BC
10.3
Mrs. VanderSpek
READING GUIDE: Convergence of a Series with Positive
Terms
NOTE: I ask you to find exercises from the text for some of these. I recommend that you
use exercises that have been assigned.
1. What is meant by a positive se
Chapter 5: Reading Guides for AP Calculus AB and BC
5.7
Mrs. VanderSpek
Further Transcendental Functions
This section just focuses on a bunch more integrals.
1. Write the definition of lnx in integral form and include a graph to explain what it means.
2.
Chapter 4: Reading Guides for AP Calculus AB and BC
4.7
Mrs. VanderSpek
Applied Optimization
Optimization problems are practical (for the most part) problems that allow us to find the optimum
solution to a problem. For example, the least cost, the maximum
AP Calculus BC
9.1
Mrs. VanderSpek
Reading Guide: Solving Dierential Equations
1. Read the first section carefully.
(a) Explain the dierence between a general solution and a particular solution to a dierential
equation.
(b) Give an example of a 3rd order
10.6: Power Series
A power series centered at x = c is written like this
F(x) = an (x c) n =a0 + a1 (x c)1 + a2 (x c)2 + a3 (x c)3 +L
n=0
Earlier, we talked about Taylor Polynomials
expanded about x =a. This is analogous.
Example in Desmos: https:/www.d