Stuff You Must Know Cold Flashcards
Formula for Area of a Circle
A=πr^2
Formula for Circumference of a Circle
C=2πr
Area of a Rectangle
A=bh
Area of a Triangle
A=1/2bh
Area of a Trapezoid
A=1/2(b1 + b2)h
Volume of a Cone
V=1/3πr^2h
Factor a^2-b^2
(a+b)(a-b) Difference of Squares
a^3-b^3
(a-b)(a^2+ab+b^2) Difference of Cubes, same, different always positive
a^3+b^3
(a+b)(a^2-ab+b^2) Sum of Cubes
What does this function look like? 1/x
VA@0, Opposite Origin, HA@0
What does f(x)=1/x^2 look like?
VA@0, HA@0, Reflection across y-axis
What does f(x)=e^x look like?
HA@0, (0,1), goes through (1, 2….)
What does f(x)=ln(x) look like?
Opposite e^x, (1,0)
What f(x)=sin(x) look like?
Starts at (0,0), (pi/2,1)
What does f(x)=cox(x) look like?
Starts at (0,1), (pi/2,0)
What does f(x)=/a^2-x^2 look like?
Semi Circle, starts at (a,0), up to (0,a), then (-a,0)
Rewrite cot(x)
1/tan(x)
Rewrite sec(x)
1/cos(x)
Rewrite csc(x)
1/sin(x)
What can 1+tan^2x substitute?
sec^2x
What can 1+cot^2x substitute?
csc^2x
What can tan(x) also be?
sin(x)/cos(x)
What can cot(x) also be?
cos(x)/sin(x)
What does ln(e)= to?
1
x^ax^b
Addition of Exponents x^a+b
x^a/x^b
Subtraction of Exponents x^a-b
(x^a)^b
Power to Power is Multiplication x^ab
x^-a
1/x^a
x^1/a
^a/x
x^0
1
ln(a) + ln(b)=
ln(ab)
ln(a) - ln(b)=
ln(a/b)
aln(b)=
lnb^a
What does the graph look like if f(x) does not exist?
Discontinuous, there is a hole at f(x)
What does the graph look like if lim of x to a f(x) does not exist?
Discontinuous, two different lines at different y values
What does the graph look like of f(a) does NOT equal lim x to a f(x)?
Discontinuous, a dot filled above the hole in the function.
What is the definition of a derivative?
lim of h to 0 f(x+h) - f(x) over h
What is the product rule?
“Right d-left plus left d-right”
What is the quotient rule?
“low d-high minus high d-low over low squared”
What is the chain rule?
f’(g(x)xg’(x)
Ex.sin(x^2)= cos(x^2)2x
derivative of sinx
cosx
derivative of cosx
-sinx
derivative of tanx
sec^2x
derivative of cotx
-csc^2x
derivative of secx
secx tanx
derivative of cscx
-cscx cotx
A function is increasing if…
f’(x) is positive
A function is decreasing if…
f’(x) is negative
A function is CCU if…
f’‘(x) is positive
A function is CCD if…
f’‘(x) is negative
A function has a maximum if…
f’(x) changes from + to -
A function has a minimum if…
f’(x) changes from - to +
A function has a point of inflection if…
f’‘(x) changes sign
