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Carbo's Calculus- When You See... [You Should think of...]
Carbo's Calculus- When You See... [You Should think of...]
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Calculus: When You See... Final Review
Flashcards
44 cards
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Practice quiz
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Questions
44
Answers
1
General Knowledge: Where does LEGO come from?
Norway
Finland
Sweden
Denmark
2
d
/
dx
∫
#
x
f(t)dt
F(t)+C
f'(x)
f(x)-f(#)
f(x)
3
Intermediate Value Theorem
f(x) must be continuous
f(c) exists if f(a)<f(c)<f(b) (or vice versa)
f(a)=value; f(b)=different value
all of the above
4
General Knowledge - What do you call a baby goat?
Kid
Goat
Grace James Binney
Baby Goat
5
show a limit exists
function must be defined
derivative must be defined
lim from left = lim from the right
f'(x)=0
6
instantaneous rate of change
1/(b-a)∫abf(x)
f'(a)
(f(b)-f(a))/(b-a)
IVT
7
Find the equation of a line tangent to f(x) at (a,b), you should think...
Find f'(a) and set = 0
Calculate the derivative.
Calcultate the 2nd derivative
Find the point (a, f(a)) and slope f'(a); use point slope
8
Integrate
Use geometry to find area under the curve
Riemann Sum or trapezoidal approximation
Antiderivative
All of the above
9
Movie Trivia:
Name this movie.
Minions
Despicable Me
Despicable Me 3
Despicable Me 2
10
Trivia: Guess this logo
Disney Channel
Chanel
Caramel
Channel
11
definition of a derivative
all of the above
f'(x)=limx→a(f(x)-f(a))/(x-a)
f'(x)=limh→0(f(a+h)-f(a))/h
f'(x)=limh→0(f(x+h)-f(x))/h
12
particle speeding up
acceleration positive
velocity/acceleration opposite signs
velocity positive
velocity/acceleration same sign
13
odd function
f(-x)=-f(x); symmetric about the origin
Symmetric about x-axis
symmetric about y=x
f(-x)=f(x); symmetric about the y-axis
14
given position, find velocity
calculate derivative
integrate twice
integrate once
calculate second derivative
15
Mean Value Theorem
f'(a) is undefined
avg rate of change = inst. rate of ch; (f must be differ.)
average rate of change = 0
instantaneous rate of change = 0
16
volumes with known cross sections (perpendicular to the x-axis)
∫cd(Area)dy
1/2(b1+b2)h
∫ab(Area)dx
f'(x)
17
chain rule: f(g(x))
f'(g(x))g'(x)
f'(g(x))+g'(x)
f'(g'(x))
f(x)g'(x)+f'(x)g(x)
18
Find critical numbers
f''(x)=0
f'(x)=0 or f''(x)=0
f'(x)=0 or f'=undefined
only f'(x)=0
19
RANDOM QUESTION
?
?
?
?
20
find the minimum value
test endpoints and critical numbers
f'(x)=0; where f'(x) switches from - to +
f'(x)=0
find cross sectional area
21
General Knowledge - What game is this?
Mario Kart
Centipede
Ms Pac Man
Donkey Kong
22
average rate of change
f'(a)
IVT
1/(b-a)∫abf(x)
(f(b)-f(a))/(b-a)
23
Rolle's Thm
avg rate of change =0
f'(c)'=0
f(a)=f(b)
all of the above
24
Trivia: 2020 was a Leap Year?
True
False
25
horizontal tangent line
f'(x)=0
f'(0)
f''(x)=0
f(x)=0; then plug into f'(x)
26
General Knowledge: How many keys on a standard piano?
88
90
92
86
27
find where f is increasing
f''(x)=0
f'(x)=0; where f' >0
f'(x)=0; where f'<0
f'(x)=0
28
General Knowledge - What is the rarest blood type?
B
A
AB - Negative
O
29
Show that f is continuous
f(x) exists at a point
limit of f(x) at point must = f(x) at that point
limit of f exists at that point
all of the above
30
General Knowledge - How often does the moon orbit the Earth?
every 7 days
every 30 days
every 365 days
every 27 days
31
horizontal asymptotes/limits to infinity
BOBO/BOTU/BETC
both numerator=0 and denominator=0
denominator=o
numerator=0
32
show that f is differentiable at x=a
both of the above
limf'(a) from the left = limit of f'(a) from the right
none of the above
f(a) is continuous
33
General Knowledge: Thomas Cup is associated with
Table tennis
Lawn tennis
Billiards
Badminton
34
even function
Symmetric about x-axis
f(-x)=f(x); symmetric about the y-axis
symmetric about y=x
f(-x)=-f(x); symmetric about the origin
35
Fundamental Theorem of Calculus
∫ab f'(x)dx = f(b)-f(a)
f'(x)=0
life is over
there must be a value between two values where f(x)=c
36
average value
(f(b)-f(a))/(b-a)
f'(a)
1/(b-a)∫abf(x)
IVT
37
General Knowledge: What is the capital of Iceland?
Nuuk
Stockholm
Reykjavik
Lulea
38
find points of inflection
f' switches from + to - or - to +
f"(x)=0, f'' changes signs
f'(x)=0 only
f''(x)=0 only
39
GENERAL KNOWLEDGE: What is the capital city of Canada?
Quebec City
Toronto
Vancouver
Ottawa
40
total distance
take the derivative of position
integrate absolute value of velocity
integrate velocity
integrate acceleration
41
Find equation of the line normal to f(x) at(a, b), you think...
point: (a,f(a)); slope=-1/f'(a); point-slope formula
take derivative, set = 0
Integrate
point: (a,f(a)); slope=f'(a); point-slope formula
42
find vertical asymptotes
every time denominator=0
where numerator = 0
leading coefficients when degree on top = degree on bottom
every time denominator = 0 in reduced form
43
Derivative of an inverse (f & g are inverse functions)
f'(a)=1/g'(b)
sin(x)=cos(x)
y=mx+b
f'(x)=g'(y)
44
This random thing.
Boo
Emoji
Dog
Number
