Unit 6 Calc gr 12

Question 1

scalar

Answer 1

quantity having size or magnitude ex. length or volume

Question 2

vector

Answer 2

quantity having size or magnitude and direction ex. force velocity, acceleration

Question 3

notation

Answer 3

vector is AB (arrow) and AB (arrow with abs bracket) is magitude

Question 4

equality of vectors

Answer 4

two vectors are equal if they have same magnitude and direction

Question 5

negative vector

Answer 5

opposite direction but same magnitude. they are parallel to each other

BA = -AB

Question 6

opposite vectors

Answer 6

two vectors that are opposite in direction but same in magnitude. AB and BA are opposites

Question 7

angle between vectors

Answer 7

is tails together

Question 8

scalar multiples

Answer 8

direction: just multiply
magnitude: ABS then multiply

Question 9

unit vector

Answer 9

has a magnitude of 1 and is the same direction as V but symbol V hat

can be expressed as v hat= 1/ABSv times V

ex. v= 20 km/hr N

v hat= 1/20 v

Question 10

geometric vectors

Answer 10

illustrated without coordinate axes ex. AB

Question 11

algebraic vectors

Answer 11

illustrated with coordinate axes ex. (1,0)

Question 12

collinear

Answer 12

when two vectors are parallel or lie on the same straight line. vectors that are collinear are not parallel.

two vectors are collinear if it is possible to find a nonzero scalar that can give the other vector’s magnitude

Question 13

draw out the special triangles w/ angle 30

Answer 13

BLACH

Question 14

draw out special triangle w/ angle 45

Answer 14

BLACH

Question 15

WRITE OUT cosine law

Answer 15

BLACH

Question 16

write out sine law

Answer 16

BLACH

Question 17

write out cosine law angle

Answer 17

BLACH

Question 18

communicative property of addition

Answer 18

a + b = B+a

Question 19

associative property of addition

Answer 19

(A +b) + C= A + (b +c)

Question 20

distributive property of addition

Answer 20

K(A + B)= Ka + Kb

Question 21

for each both the vectors shown, determine the components of the related position vector

Answer 21

do OF-OE then do magnitude

Question 22

when asked to prove a right angle triangle

Answer 22

pythagorean theorem must work

Question 23

parallel vectors have

Answer 23

parallel vectors have scalar multiplied coordinates ex. 2(1,1) is paralell to (2,2)

Question 24

in limits

Answer 24

include the f(x) part, include the 0/0 and cts check

Question 25

difference of cubes formula

Answer 25

(a-b)(a2+ab+b2)

Question 26

CHAIN RULE

Answer 26

F’(G(x))* g’(x)

Question 27

to be differentiable

Answer 27

cts and limit from the right equals the left

Question 28

local extrema

Answer 28

f’(x)= o, DNE (no endpoint but it includes absolute min/max)

Question 29

to find extrema

Answer 29

test critical values and endpoints

Question 30

optimization

Answer 30

2l –>squared–> (2l)2 and then you have to divide the answer by two as well!

Question 31

graphing

Answer 31

when checking f’(x)=o, include vertical asymptotes