The Chain Rule.
A composite function uses the output of one function for the input of the other function: f(g(x)).
Trig stuff, and note the use of the SQUEEZE THEOREM at the end
Proof of limit of sin(x) over x
Derivatives- Displacement, Velocity, Acceleration
Anti- Derivative= integral= undoing the derivative
Parametric Mode
-Can be changed under MODE menu. Click PAR
-Can be used for particle problems to analyze a one or two dimensional motion
-Easier to see if you use the bouncing ball when you graph it
-You can plot displacement, velocity (derivative of displacement), and acceleration (2nd derivative of displacement [...]
CLASS OCTOBER 14 2009
WE GOT OUR TESTS BACK
THEY WERE SCALED
QUESTIONS THAT WE WENT OVER:
PART 1: 2,4,6,7
QUESTION 2: REMEMBER TO FACTOR OUT AS MUCH AS POSSIBLE-SYNTHETIC DIVISION ON CUBIC. ANSWER B
QUESTION 4, WHAT DOES THIS FUNCTION LOOK LIKE?
ANSWER: C
THE LIMIT OF THE FUNCTION APPROACHING INFINITY IS ZERO, SO THE X AXIS IS THE VERTICAL ASYMPTOTE.
THE DENOMINATOR [...]
Binomial Expansion
Example:
Definition of Derivative: f ‘ (x)
Forward Difference (quotient difference)=
Backward Difference=
Symmetric Difference (often used with table)=
At a Point=
Derivative Worksheet:
1.
2.
f’(x)=(-2)
POWER FUNCTION RULE (also on page 92)
Power function continued…
Example 1
Example 2
Calculator:
On the AP exam, a calculator can be used for finding x intercepts, numerical derivatives and numerical integration.
To find the derivative at x=2 when f(x)=x^5:
Plug [...]
finds the slope of the tangent line at f=c
more specific; at a point
use when you have a function and a point
any function at any point
can be used for every problem
as x and x+h get closer, it approaches the slope of the tangent line.
Derivative: Slope of the tangent line.
Find when taking limit of the slope of [...]
