Limits
What is a limit?
A predicted Y-Value
What is a derivitive?
A limit
What are C# in mathematical terms?
When the derivative equals 0/DNE
The anti-derivative is..
The opposite of the derivative.
In Mr. Allen class, what mode should we put in our calculator?
Radians
The limit when x-> 2 of (x+3)
5
4x +5
When do we know if f(x) is increasing?
When f'(x) is positive.
If f'(x) = 6x2+12x and f(2) = 2, find f(x)
f(x) = 2x3+ 6x2 -38
dy/dx of ex
ex
The limit when x→3 of (x−3)/(x2−9)
1/6
The function is continuous, it is differentiable
False
1st Derivative test is...
To determine where a function has local maxima, minima, or neither using the derivative .
What does Intergals tell us?
It tell us the area.
How do we find the derivative of Y1 on a calculator?
1. Press "2nd"
2. Press "Trace" or "Calc"
3. Press "6"
4. Select any X value.
The 1st rule of Continuity is...
f(x) has to be defined.
dy/dx tan(x)
sec(x)2
What are the rules when MVT applies?
1. Continuous on [a,b]
2. Differentiable on (a,b)
5
∑ (2x2+3)
x=1
125
dy/dx arctan(x)
1/(1+x2)
The limit equation of a Horizontal Asymtope...
The limit when x→∞ of f(x)
dy/dx (x3+1)/(2x-5)
Time Limit: 40 seconds
y′=(4x3−15x2−2)/(2x-5)2
Define the 2nd derivative test and tell us when does the 2nd Derivative Test fails?
To determine whether a critical point of a function is a local maximum, minimum, or inconclusive, using the second derivative. It fails when f"= 0
n
What is ∑ (x)
x=1
(n(n+1))/2
How does limits, Derivatives, and Integrals all connect each other?
Because of the Fundamental Theorem of Calculus (FTC)