PR.1
|
RELATED RATES
I can solve applied problems involving related rates, including setting up a problem based on a written description, differentiating implicitly and solving for a given quantity or rate. |
Answers to Related Rates Packet
(available in the attachments at the bottom too)
|
PR.2
|
OPTIMIZATION
I can solve basic optimization problems including setting up equations for the volume and area of simple shapes and solids. |
Answers to Related Rates Packet
(available in the attachments at the bottom too)
|
PR.3
|
LOGARITHMIC DERIVATIVES
I can differentiate functions involving the natural logarithmic function
and can apply the technique of logarithmic differentiation to
differentiate algebraically complicated expressions.
|
Video about logarithmic differentiation. Also available here and on Al-Khazneh.
|
PR.4
|
LOGARITHMIC INTEGRALS
I can use the Log Rule of Integration to integrate a rational function and can use this to integrate trigonometric functions.
|
|
PR.5
|
EXPONENTIAL CALCULUS
I can differentiate and integrate natural exponential functions. |
Deriving the fact that d/dx[e^x] = e^x
|
PR.6
|
"UNNATURAL" BASES
I can differentiate and integrate exponential functions of a base other than e. |
Class Notes for "Unnatural Bases":
|
PR.7
|
SLOPE FIELDS
Given a differential equation, I can draw a
slope field and sketch a particular solution through a given point. I
can also match a slope field with a differential equation and
vice-versa. |
Video about slope fields. Also available here and on Al-Khazneh.
|
PR.8
|
DIFFERENTIAL EQUATIONS
Given a separable differential equation, I
can solve for the general solution and plug in initial conditions to
find a particular solution. |
The three most important tricky situations you might encounter in solving diffEQs:
1. Flipping a whole expression
ex: dy/dx = x^3y^2 through (0,2)
Answer: y = 4/(2-x^4)
2. Choosing the correct branch of a solution when you take a square root
ex: dy/dx = x^3/y through (1,-1)
Answer: y = -sqrt(x^4/2+1/2)
3. Dealing with constants and exponential functions
ex: dy/dx = y/x^2 through (-1,4e)
Answer: y = 4e^(-1/x)
|
PR.9
|
MODELS
I can use specific differential equations
to model exponential decay and growth, and can perform a range of tasks
with the equation that I create (including solving for variables)
|
Video about an important exponential models. Also available here and on Al-Khazneh.
|
PR.10
|
INVERSE FUNCTIONS
I can prove that a function has an inverse
by showing that it's monotonic and can find the inverse in many cases.
Also, given information about the slope of a function, I can calculate
the slope of its inverse. |
Drill on finding the tangent line to a given point for an inverse function:
http://archives.math.utk.edu/visual.calculus/3/inverse.1/index.html
Notes from class on review/pre-cal topics:
|
PR.11
|
INVERSE TRIG FUNCTIONS
I can evaluate values of arcsin, arccos and
arctan by hand, noting their domain and range, and can differentiate
functions involving these three functions |
Arctrig evaluation practice (not derivatives!)
Multiple Choice Review/Practice for PR.10 and PR.11:
|
