Sequences & Series
Recursive formula definition?
Defines a term using previous term(s).
Meaning of limx→a f(x)=L
As x approaches a, f(x) approaches L.
What does the derivative represent?
Instantaneous rate of change (slope of tangent line).
Amplitude of y=asin(bx+c)+d?
|a|
Law of Sines?
a/sinA =b/sinB = c/sinC
How do you generate terms from a recursive rule?
Start with the initial value and repeatedly apply the rule.
When does a limit exist?
When left-hand and right-hand limits are equal.
Interpretation of T′(4)=120?
The station is producing toys at 120 toys/hour at 4 hours.
Midline of y=asin(bx+c)+d?
y = d
Law of Cosines?
Sum of the first n terms of an arithmetic sequence?
Sn=n/2(a1+an)
Conditions for continuity at x=a?
f(a) exists, limx→a f(x) exists, and they are equal.
Derivatives Power Rule
Maximum value of a sinusoidal function?
d + |a|
Area of a triangle using two sides and the included angle?
A=1/2absinC
How do you solve a system of three equations?
Elimination or substitution.
What does differentiable imply?
The function is continuous
Derivative of cosx?
−sinx
Minimum value of a sinusoidal function?
d - |a|
When do we use the law of sines?
SAA or ASA
What does a solution to a system represent?
A point that satisfies all equations simultaneously.
What does continuous imply about f(a)?
f(a) exists.
Derivative of sinx?
cosx
How do you find the period of a sinusoidal function?
Use P= 2pi/b
When do we use the law of cosines?
SSS or SAS