Change Short Answers

Question 1

When was calculus invented?

Answer 1

End of 1600’s . 1687

Question 2

Before Newton, how were mathematical models
created?

Answer 2

Trying to match what was observed

Question 3

Name two scientists who influenced Newton.

Answer 3

Galileo, Kepler, Fermat, Pascal, Cavalieri

Question 4

Why did Newton learn math?

Answer 4

To do astrology

Question 5

What was Newton’s first paper about?

Answer 5

Light is made up of many colors

Question 6

Why was Newton reluctant to publish Principia?

Answer 6

His first paper was mocked . No one liked his first paper

Question 7

Who published Newton’s book?

Answer 7

Sir Edmund Halley

Question 8

How did Halley convince the world that Newton’s
theories were correct?

Answer 8

By predicting Halley’s Comet

Question 9

How does Calculus predict the future?

Answer 9

If you know where something is and how it will change, you know what it will be.

Question 10

How does Calculus create the future we want?

Answer 10

If you know what you want, you can “run” change backwards and calculate what needs to be now to get there.

Question 11

List the two conflicting rules that suggest 0/0 is an
indeterminate.

Answer 11

0/# = 0, #/0 = “∞”

Question 12

Rules that conflict for 0^0.

Answer 12

0^# = 0, #^0 = 1

Question 13

What rules conflict for ∞/∞.

Answer 13

∞/# = ∞, #/∞ = 0

Question 14

For ∞ – ∞

Answer 14

∞ – # = ∞ | # – ∞ = –∞

Question 15

Define Δ x

Answer 15

x_1 - x_0

Question 16

Intuitiely what is Δ x

Answer 16

The Change in x

Question 17

What does negative change mean?

Answer 17

Its going down

Question 18

Express Δ S as a function of t_1 and t_0

Answer 18

Δ S = S(t_1) - S(t_0)

Question 19

Express Δ S as a function of t and Δ t

Answer 19

Δ S = S(t+Δ t) - S(t)

Question 20

Intuitively, why is t_1 = t_0 + Δ t

Answer 20

t_1 is the new value of t is the old value plus ohow much it changed

Question 21

Is Δ miles = 10 a lot?

Answer 21

Depends. The close, short, are relative and mean nothing

Question 22

Express miles per hour in Δ notation

Answer 22

Δ miles/Δ hours

Question 23

Intuitively, what does Δ $/Δ Hour represent?

Answer 23

Dollars per hour or salary

Question 24

What’s the numeric value of Δ Inches/Δ Feet?

Answer 24

Inches per foot or 12

Question 25

Express slope in terms of Δ x and Δ y

Answer 25

Δ y/Δ x

Question 26

Express slope in terms of x_0, x_1, y_0, y_1 (What's the basic slope equation?)

Answer 26

y_1 - y_0 / x_1 - x_0

Question 27

Instantaneous change is the slope of the _____ line at the point

Answer 27

tangent line

Question 28

average change is the slope of the_______ between two points

Answer 28

secant

Question 29

the technical term for instaneous change

Answer 29

derivative

Question 30

to find the instananeous change we let Δ x go to what?

Answer 30

0

Question 31

Intuitievly what is 5/0?

Answer 31

some kind of ∞

Question 32

0/0 is what?

Answer 32

indeterminate

Question 33

what is an indeterminate

Answer 33

an expression where value is uncertain and rules conflict such as 0/0, ∞/∞, ∞-∞, 1^∞

Question 34

Symbolically say “as x gets close to 4, 3x gets close to 12”.

Answer 34

lim 3x = 12 x->4

Question 35

What’s the symbolic definition of derivative of f(x)?

Answer 35

lim Δf/Δx or lim f(x+Δx) - f(x) Δx->0 Δx->0

Question 36

What’s the symbolic definition of dy/dx?

Answer 36

lim Δ𝑦/Δ𝑥 Δ𝑥→0

Question 37

The slopes of the _____ get closer & closer to the slope of the _________ as x gets close to 0.

Answer 37

secants, tangent

Question 38

If f(x) = x^2 + x, give the general form of a point on f.

Answer 38

(x, x2 + x)