AP Calculus AB/BC
3.5 Derivatives of Trig Functions, p. 141
Consider the function
y sin
We could make a graph of the slope:
slope
1
2
0
0
1
0
Now we connect the dots!
2
The resulting curve is a cosine curve.
1
d
sin x cos x
dx
We can do the same thing f
AP Calculus AB/BC
1.1 Lines, p. 3
Lines and equations of lines are used in numerous business
and economic applications.
Linear functions are taught beginning with Algebra 1 and
continuing all throughout Calculus.
Our first definition in Calculus is Increm
AP Calculus AB/BC
Chapter 1 Review
Prerequisites for Calculus
Linear Equations
Point-Slope Equation: y m x x1 y1
Slope-Intercept Form: y = mx + b
Parallel Lines: Slopes are equal
Perpendicular lines: Slopes are Opposite
Reciprocals
Functions and Graph
AP Calculus AB/BC
3.1 Derivatives of a Function, p. 98
In section 2.4, the slope of the curve of y = f(x) was defined
at the point where x = a to be
lim
f a h f a
h
h 0
This limit is also called the derivative of
We write:
f x lim
h 0
f
at a.
f x h f x
h
Chapter 3:
Water and the Fitness of
the Environment
Water
Polar~ opposite ends, opposite charges
Cohesion~ H+ bonds holding molecules
together
Adhesion~ H+ bonds holding molecules to
another substance
Surface tension~ measurement of the difficulty
to
8.2 LHpitals Rule,
p. 444
Actually, LHpitals Rule was
developed by his teacher
Johann Bernoulli. De lHpital
paid Bernoulli for private
lessons, and then published the
first Calculus book based on
those lessons.
Guillaume De l'Hpital
1661 - 1704
8.2 LHpita
AP Calculus AB/BC
1.2 Functions, p. 12
Engineers use functions to optimize designs in both form and
function.
Definition: Function
A function is a rule (usually an equation) that assigns a unique
value in the Range, R, to each value in the Domain, D.
D =
Chapter 4~
Carbon &
The Molecular
Diversity of Life
Organic chemistry
Biological thought:
Vitalism (life force outside physical &
chemical laws) Berzelius
Mechanism (all natural phenomena
are governed by physical & chemical
laws) Miller
Carbon
tetravalen
Chapter 5~
The Structure &
Function of
Macromolecules
Polymers
Covalent monomers
Condensation reaction
(dehydration reaction):
One monomer provides a
hydroxyl group while the other
provides a hydrogen to form a
water molecule
Hydrolysis:
bonds between