Formula Sheet Flashcards
Derivative definition
L’hopital Rule
Average rate Δ
Avg Value
Top heavy:
slant asymptote/diverge (long division)
Bottom heavy:
y = 0
Degree N = D (balanced)
Ratio of Coeff
Fundamental th. Calc 1
Fundamental Th. Calc 2
The Extreme-Value Theorem:
If continuous [a,b] then must have absolute max & min
The Mean Value Theorem
If continuous on [a,b] and differentiable (a,b)
- Average rate of change = slope tangent line at some point
Rolle’s Theorem (special case MVT)
If continuous on [a,b] and differentiable (a,b)
HORIZONTAL tangent line at some point
Intermediate Value Theorem:
- If continuous on [a,b] and f(a) ≤ x ≤ f(b)
Trig
Chain Rule
Point of inflection
concavity changes or f’‘(x) changes sign
Volume of Solids with Known Cross-Sections
Volume of Solids with Known Cross-Sections
EQUILIATERAL TRIANGLE
Volume of Solids with Known Cross-Sections
SEMI CIRCLE
Area between two graphs
Arc Length
Polar to rectangular
Rectangular to polar
Arc Length Parametric
Arc Length of a Polar curve
Area enclosed by a polar curve
Second Derivative of Parametric
Acceleration Vector
Speed of Parametric
Total Distance Parametric
integral of velocity (V)
Sum of an Infinte Geometric Series
Nth term Test
Geometric Series Test
P-series
Alternating series
Alternating Series Error Bound
Ratio Test
CHECK ENDPOINTS
Direct Comparison
If bigger series C, smaller must also C
If smaller series D, bigger must also D
Limit Compairson Test
either both series C or D
Absolutely Convergent
Taylor Series
Lagrange Error Bound
M for sin and cos = 1
Elementary Function: e^x
Elementary Function: cosx
Elementary Function: sinx
Elementary Function: 1 / (1-x)
Reiman Sums
Trapezoidal Sum
