AP Calculus
Chapter 3
Derivatives
3.1 Derivative of a Function
Derivative
f ( x h) f ( x )
f ' ( x) lim
h 0
h
If f(x) exists then f(x) is differentiable
Differentiable Functions are differentiable at every
point in their domain.
3.1 Derivative of a Functi
handkerchief a couple of times with the right hand, leave the
half dollar behind the folds of the cloth, gripping it by the tip of
the left thumb, Fig. 11. Bobo's Coin Magic Presented by
www.learnmagictricks.org Page 469 Now lower the hands to
the positio
the upper coin a quarter inch, Fig 1. It is necessary to hold the
coins exactly in this manner to facilitate the move. Now as you
throw the handkerchief over the coins, raise Bobo's Coin Magic
Presented by www.learnmagictricks.org Page 463 the right
hand
is concealed in the right thumb palm.) An easy, careless
handling of the right hand at all times will convince the most
skeptical spectator that the hand is empty. Phase Three Allow a
moment for the spectators to grasp what has Bobo's Coin Magic
Presented
as the right hand returns the front edge of the handkerchief to
its original position the left hand is lowered and the portion
from the left forearm falls forward also. This simultaneous
action should appear to the spectators as though you merely
raised t
her the coin and handkerchief to hold, transfer them to your
right hand as follows: With the right forefinger and thumb grip
the right edge of the silver coin through the cloth, Fig. 1, then
curl the second, third and fourth fingers around the
handkerchie
Presented by www.learnmagictricks.org Page 488 that effect. As
you do this, drop the coin from the right hand into his upper
breast coat pocket. (More nerve than skill is required to
perform this loading operation, but once the knack is acquired
it is eas
left and one which was already there. Again shift the finger
palmed coin in the left hand to classic palm position as you
exhibit the three coins in the right. Place them back in the left
hand as you did the others, the coins going on the curled
fingers.
palmed. Secure the blob of wax on the tip of the right second
finger. Then take one of the quarters from the left hand and as
you display it momentarily, press the wax to its back. You are
now showing a coin in each hand. Place the left hand's quarter
in
aid of a pair of pliers bending the protruding half slightly. Have
the bent penny finger palmed in your right hand as you ask for
the loan of a penny. Receive the penny in your left hand. Then
pick it up with your right fingers and thumb and toss it back
but be careful that the two coins do not clink together in this
action. (See The Coin Flip.) This subtle move shows without
saying that the right hand is otherwise empty. Holding the
visible coin between the first finger and thumb of the right
hand, lower
the coin into the palm, then take up the Bobo's Coin Magic
Presented by www.learnmagictricks.org Page 425 glass and hold
it as described. Hold the hands far apart and repeat the same
set of movements to effect passage of the last coin. Finally open
the le
show the right hand containing the three coins. Count them
onto the table, and show the hands empty, without calling
attention to them verbally. Three times you have placed a half
dollar in your pocket. Three times the coin returns to join the
other two.
the onlookers. The right hand takes up the glass, and in doing so
shifts the retained coin to the classic palm, Fig. 8. The left hand
closes on the four coins, and the right hand releases the palmed
coin, and it falls into the glass. The right hand places
is removed from the table, it and the one concealed in the right
hand are dropped together into the cup as one. Just toss them
Bobo's Coin Magic Presented by www.learnmagictricks.org Page
433 together, that's all. Finally, the right hand takes the last co
mind and reply, "Two." Slap the five coins onto the table to
show two in the left hand and three in the right hand, as you
say, "No. Stop guessing!" By now he is thoroughly muddled.
Regardless of his reply set the stage for the phase and give him
another
where silver dollars are readily procurable you might begin the
trick by borrowing the coins. In any event, have them marked
for identification by three different spectators. Show the glass
empty and as you place it in the right side pocket adjust the end
Presented by www.learnmagictricks.org Page 402 Three and
Three Because of its simplicity, this has become one of my
favorite "coin pass" effects. I hope it will become one of yours,
too. Effect: Three coins pass one at a time from the left hand to
join th
one of my best coin illusions. Ever since I first read the "Coins to
Glass" in Tommy Downs' book way back in 1908, I have been
fascinated with the possibilities this feat offers. Other ways of
performing the trick have appeared in The Sphinx and some in
T
four coins. Show your hands empty, close them into a loose fist
and then turn them backs up. Start at the inner end of the two
rows and work outward. Use the thumb and second joint of the
first finger of each hand to pick up the first two coins, Fig. 1,
B
AP Calculus
Chapter 2
Limits and Continuity
2.1 Rates of Change and
Limits
Average vs. Instantaneous Speed
Average is during a time interval (ex: during first 3
seconds)
Instantaneous is at a certain instant (ex: at 3
seconds)
Example 1:
a.
A rock breaks
AP Calculus
Chapter 1
Prerequisites for Calculus
1.1 Lines
General Equations for Lines
y y1 m( x x1 )
Point Slope:
Slope Intercept:
General Linear Equation:
y mx b
ax by c
1.1 Lines
Slope m = y
x
change in y over change in x
Parallel Lines have same slope
AP Calculus
Chapter 4
Applications of Derivatives
4.1 Extreme Values of Functions
Absolute Extremes (min and max) can only occur at one place on
the interval (also called global)
Local Extremes can occur at several places on the interval (also
called rela
AP Calculus
Chapter 7
Applications of Definite Integrals
7.1 Integral as Net Change
We are going to focus on how to set up a function to be
integrated
Example 1: The function v(t) is the velocity in m/sec
of a particle moving along the x-axis.
a)
b)
c)
De
The Definite Integral
Chapter 5
AP Calculus
5.1 Estimating with Finite
Sums
RAM Rectangular Approximation
Method
LRAM left hand endpoint
RRAM right hand endpoint
MRAM midpoint
We are going to create rectangles under
irregular curves to estimate areas and
DERIVATIVES - TRIG FUNCTIONS
1. f (x) = 4(cos x)
2. f (x) = 3x(sin x)
f '(x) = 3sin x + ( cos x ) 3x
f '(x) = 4 sin x
f '(x) = 3( sin x + x cos x )
3. f (x) = x 3 (sin x)
4. f (x) = x x 2 (cos x)
f '(x) = 3x 2 ( sin x ) + ( cos x ) x 3
f '(x) = 1 2x cos x