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Digitopolis - The Land of Numbers
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Differentiate
Differentiate
Differentiate
Differentiate
Differentiate
Differentiate
Differentiate
y=sin(x)
Differentiate
y=cos(x)
What is the Tangent Line Equation?
Differentiate
Differentiate
ReWrite
Rewrite
Differentiate
y=f(g(h(x)))
Differentiate
y=log(x)
Rewrite
Differentiate
y=sec(x)
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?
Differentiate
y=tan(x)
Differentiate
y=csc(x)
Differentiate
y=cot(x)
Differentiate
y=sec(x)
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
cos(x)sin(x)=?
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:
0/0
or
Infinity/Infinity
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"?
1-
2-
3-
4-
5-
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 area of a cylinder?
The area of the top and bottom:
Plus the area of the sides:
Formula
What is the volume of a cube?
Author
mattrcherry
ID
211333
Card Set
Digitopolis - The Land of Numbers
Description
This is a Calculous Study Guide for my Cal 1 class.
Updated
2013-04-11T05:20:16Z
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