Equations

Question 1

Define Δ x

Answer 1

x_1 - x_0

Question 2

Intuitiely what is Δ x

Answer 2

The Change in x

Question 3

What does negative change mean?

Answer 3

Its going down

Question 4

Express Δ S as a function of t_1 and t_0

Answer 4

Δ S = S(t_1) - S(t_0)

Question 5

Express Δ S as a function of t and Δ t

Answer 5

Δ S = S(t+Δ t) - S(t)

Question 6

Intuitively, why is t_1 = t_0 + Δ t

Answer 6

t_1 is the new value of t_0 is the old value plus hoe much it changed

Question 7

Express miles per hour in Δ notation

Answer 7

Δ miles/Δ hours

Question 8

Intuitively, what does Δ $/Δ Hour represent?

Answer 8

Dollars per hour or salary

Question 9

Express slope in terms of Δ x and Δ y

Answer 9

Δ y/Δ x

Question 10

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

Answer 10

y_1 - y_0 / x_1 - x_0

Question 11

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

Answer 11

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

Question 12

What’s the symbolic definition of dy/dx?

Answer 12

lim Δ𝑦/Δ𝑥
Δ𝑥→0

Question 13

If f(x) = x2 + x, give the general form of a point on f.

Answer 13

(x, x2 + x)

Question 14

What can you multiply √𝑥−√𝑦 by to get rid of the
roots?

Answer 14

√𝑥+√𝑦

Question 15

What can you multiply √𝑥+√𝑦 by to get rid of the
roots?

Answer 15

√𝑥−√𝑦

Question 16

What can I multiply cos x – 1 by to turn it into sines?

Answer 16

cos x + 1 bc cos^2 (x) -1 = sin^2 (x)

Question 17

Instantaneous Change Equation/Definition of Derivative

Answer 17

f(x) = f(x+Δ x) - F(x) all over Δ x

Question 18

f_1 Approximation Equation

Answer 18

f_1 ≈ f_0 + f_0’Δx