Digitopolis  The Land of Numbers
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Differentiate


Differentiate

Differentiate

Differentiate

Differentiate

Differentiate



What is the Tangent Line Equation?

Differentiate

Differentiate


ReWrite

Rewrite

Differentiate
y=f(g(h(x)))


Rewrite


Differentiate
y=log(g(x)
or

Rewrite
log(ab)=?
log(ab)=log(a)+log(b)

Rewrite

Rewrite

Differentiate

Differentiate
y=arcsin(x)

Differentiate
y=arcsec(x)


Rewrite

Differentiate
y=arctan(x)

Rewrite

ReWrite

Rewrite

Rewrite

Rewrite

Tangent Line Formula:

What is the Normal Line Formula?





Rewrite
sin(a+b)=?
sin(a+b)=cos(a)sin(b)+sin(a)cos(b)

Rewrite
sin(2x)=?
sin(2x)=sin(x+x)
=
sin(x)cos(x)+cos(x)sin(x)

Solve

Solve


Rewrite
sin(x)sec(x)=?
sin(x)sec(x)=tan(x)

Functions:
In what "form" will a function become a Vertical Asymptote?

Functions
In what "form" will a function have a hole?
When a point is undefined.

Functions:
Describe a Polynomial
A smooth, well behaved function.
Ex:

Functions:
Describe a Rational Function.
A polynomial multiplied, or divided by, another polynomial.
Ex:

Functions:
Describe an exponential function.
A function whose variable is the exponent of the function.

Functions:
Describe a Horizontal Asymptote.
When a function's limit as it approaches positive or negative infinity is a real number, that is it's Horizontal Asymptote.

Rewrite

Functions:
What are some of the other terms for a prime function?
The derivative of a function.
The rate of change(at a given point) of a function.
The slope of a function.
The velocity of a function.

Differentiate
Rewrite and Differentiate:
Since conventional methods would have messy results, rewrite your function.

Trig Functions
Give 3 different trig variations for this function:
Sin(x)
Tan(x)Cos(x)
1/Csc(x)
Tan(x)/Sec(x)

l' Hopital's Rule
In what two function scenarios can you implement the l' Hopital's Rule?
When the functions are of the forms:

Volume
What is the volume of a cone?

l' Hopital's Rule
What effect does l' Hopital's Rule have on your function?

l' Hopital's Rule
What are the 5 indeterminate "forms"?

Functions
Extreme values of a function only occur at what points(p)?
or when P is a boundary point of f's domain.

Multiplicity
What occurs when a function passes through a critical point where the multiplicity is even?
It changes signs.
 From + to 
 or
 From  to +

Area
What is the Area of a triangle?

Area
What is the Area of a circle?

Circumference
What is the circumference of a circle?

Memory Tools
Some Old Hags...
Can't Always Hide
Their Old Age

Optimization
What points are of most interest to you when working with Optimization?
Critical Points and Endpoints.

Volume
What is the volume of a cylinder?

Volume
What is the volume of a sphere?

Area
What is the area of a sphere?

Diameter
What is the diameter of a circle or sphere?

Formula
What is the distance formula?

Formula
What is the Area of a square?
A=xy

Logarithms

Functions

Logarithms
Log(1)=?
Log(1)=0


Formula
What is the volume of a cube?