Unit 6 Calc gr 12 Flashcards
scalar
quantity having size or magnitude ex. length or volume
vector
quantity having size or magnitude and direction ex. force velocity, acceleration
notation
vector is AB (arrow) and AB (arrow with abs bracket) is magitude
equality of vectors
two vectors are equal if they have same magnitude and direction
negative vector
opposite direction but same magnitude. they are parallel to each other
BA = -AB
opposite vectors
two vectors that are opposite in direction but same in magnitude. AB and BA are opposites
angle between vectors
is tails together
scalar multiples
direction: just multiply
magnitude: ABS then multiply
unit vector
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
geometric vectors
illustrated without coordinate axes ex. AB
algebraic vectors
illustrated with coordinate axes ex. (1,0)
collinear
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
draw out the special triangles w/ angle 30
BLACH
draw out special triangle w/ angle 45
BLACH
WRITE OUT cosine law
BLACH
write out sine law
BLACH
write out cosine law angle
BLACH
communicative property of addition
a + b = B+a
associative property of addition
(A +b) + C= A + (b +c)
distributive property of addition
K(A + B)= Ka + Kb
for each both the vectors shown, determine the components of the related position vector
do OF-OE then do magnitude
when asked to prove a right angle triangle
pythagorean theorem must work
parallel vectors have
parallel vectors have scalar multiplied coordinates ex. 2(1,1) is paralell to (2,2)
in limits
include the f(x) part, include the 0/0 and cts check
difference of cubes formula
(a-b)(a2+ab+b2)
CHAIN RULE
F’(G(x))* g’(x)
to be differentiable
cts and limit from the right equals the left
local extrema
f’(x)= o, DNE (no endpoint but it includes absolute min/max)
to find extrema
test critical values and endpoints
optimization
2l –>squared–> (2l)2 and then you have to divide the answer by two as well!
graphing
when checking f’(x)=o, include vertical asymptotes
