Exam

Question 1

What is a derivative

Answer 1

The derivative of a function f at a point (x,f(x)) is f(x+h)… if the limit exists.
This method of determining the derivative is sometimes referred to as first principles

Question 2

Average Rate of Change

Answer 2

Y2-Y1 / X2-X1

Question 3

Instantaneous Rate of Change

Answer 3

lim h->0 f(x+h)-f(x) / h

Question 4

Circle Area

Answer 4

Pi(r)^2

Question 5

Scalar

Answer 5

Magnitude

Question 6

Vector

Answer 6

Magnitude and direction

Question 7

Force of gravity

Answer 7

Fg=mg

Question 8

Force triangle

Answer 8

40* downhill (FII)
Gravity (Fg)
90* (FL)

Question 9

Component Form

Answer 9

->
OP = [x, y]

Question 10

Unit Vector Form

Answer 10

->
OP = xî + yj

Question 11

A (x1, y1) and B (x2, y2)

Answer 11

->
AB= [x-x, y-y]

->
|AB|= square root

Question 12

Determine |AB + BC|

Answer 12

First AB + BC -> [a, b]
Then square root

Question 13

Normalizing Vectors

Answer 13

u= [a, b, c]
û= abc/ |u|

Question 14

Direction Angle

Answer 14

cos a/|u|

Question 15

Dot Product

Answer 15

a•b=|a||b|cos0

Question 16

Dot product 2

Answer 16

u•v= (x•x)+(y•y)

Question 17

Cross product

Answer 17

axb= |a||b|sin0

Question 18

Cross product 2

Answer 18

middle right left middle
Cross
Multiply and substitute
[a, b, c]

Question 19

Normal [] and point ()

Answer 19

Ax+By+c=0

Question 20

Normal of [-4,-8]

Answer 20

n=[-8,4]

Question 21

Write a vector equation of the line

Answer 21

r=[x,y]+t[m,m]
X=1 put in equation for y
m= [m2, -m1]