Change Short Answers Flashcards
When was calculus invented?
End of 1600’s . 1687
Before Newton, how were mathematical models
created?
Trying to match what was observed
Name two scientists who influenced Newton.
Galileo, Kepler, Fermat, Pascal, Cavalieri
Why did Newton learn math?
To do astrology
What was Newton’s first paper about?
Light is made up of many colors
Why was Newton reluctant to publish Principia?
His first paper was mocked . No one liked his first paper
Who published Newton’s book?
Sir Edmund Halley
How did Halley convince the world that Newton’s
theories were correct?
By predicting Halley’s Comet
How does Calculus predict the future?
If you know where something is and how it will change, you know what it will be.
How does Calculus create the future we want?
If you know what you want, you can “run” change backwards and calculate what needs to be now to get there.
List the two conflicting rules that suggest 0/0 is an
indeterminate.
0/# = 0, #/0 = “∞”
Rules that conflict for 0^0.
0^# = 0, #^0 = 1
What rules conflict for ∞/∞.
∞/# = ∞, #/∞ = 0
For ∞ – ∞
∞ – # = ∞ | # – ∞ = –∞
Define Δ x
x_1 - x_0
Intuitiely what is Δ x
The Change in x
What does negative change mean?
Its going down
Express Δ S as a function of t_1 and t_0
Δ S = S(t_1) - S(t_0)
Express Δ S as a function of t and Δ t
Δ S = S(t+Δ t) - S(t)
Intuitively, why is t_1 = t_0 + Δ t
t_1 is the new value of t is the old value plus ohow much it changed
Is Δ miles = 10 a lot?
Depends. The close, short, are relative and mean nothing
Express miles per hour in Δ notation
Δ miles/Δ hours
Intuitively, what does Δ $/Δ Hour represent?
Dollars per hour or salary
What’s the numeric value of Δ Inches/Δ Feet?
Inches per foot or 12
Express slope in terms of Δ x and Δ y
Δ y/Δ x
Express slope in terms of x_0, x_1, y_0, y_1 (What’s the basic slope equation?)
y_1 - y_0 / x_1 - x_0
Instantaneous change is the slope of the _____ line at the point
tangent line
average change is the slope of the_______ between two points
secant
the technical term for instaneous change
derivative
to find the instananeous change we let Δ x go to what?
0
Intuitievly what is 5/0?
some kind of ∞
0/0 is what?
indeterminate
what is an indeterminate
an expression where value is uncertain and rules conflict such as 0/0, ∞/∞, ∞-∞, 1^∞
Symbolically say “as x gets close to 4, 3x gets close to
12”.
lim 3x = 12
x->4
What’s the symbolic definition of derivative of f(x)?
lim Δf/Δx or lim f(x+Δx) - f(x)
Δx->0 Δx->0
What’s the symbolic definition of dy/dx?
lim Δ𝑦/Δ𝑥
Δ𝑥→0
The slopes of the _____ get closer & closer to the slope
of the _________ as x gets close to 0.
secants, tangent
If f(x) = x^2 + x, give the general form of a point on f.
(x, x2 + x)
