Formula Sheet

Question 1

Derivative definition

Answer 1

Question 2

L’hopital Rule

Answer 2

Question 3

Average rate Δ

Answer 3

Question 4

Avg Value

Answer 4

Question 5

Top heavy:

Answer 5

slant asymptote/diverge (long division)

Question 6

Bottom heavy:

Answer 6

y = 0

Question 7

Degree N = D (balanced)

Answer 7

Ratio of Coeff

Question 8

Fundamental th. Calc 1

Answer 8

Question 9

Fundamental Th. Calc 2

Answer 9

Question 10

The Extreme-Value Theorem:

Answer 10

If continuous [a,b] then must have absolute max & min

Question 11

The Mean Value Theorem

Answer 11

If continuous on [a,b] and differentiable (a,b)

• Average rate of change = slope tangent line at some point

Question 12

Rolle’s Theorem (special case MVT)

Answer 12

If continuous on [a,b] and differentiable (a,b)

HORIZONTAL tangent line at some point

Question 13

Intermediate Value Theorem:

Answer 13

• If continuous on [a,b] and f(a) ≤ x ≤ f(b)

Question 14

Trig

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Chain Rule

Answer 17

Question 18

Point of inflection

Answer 18

concavity changes or f’‘(x) changes sign

Question 19

Volume of Solids with Known Cross-Sections

Answer 19

Question 20

Volume of Solids with Known Cross-Sections

EQUILIATERAL TRIANGLE

Answer 20

Question 21

Volume of Solids with Known Cross-Sections

SEMI CIRCLE

Answer 21

Question 22

Area between two graphs

Answer 22

Question 23

Arc Length

Answer 23

Question 24

Polar to rectangular

Answer 24

Question 25

Rectangular to polar

Answer 25

Question 26

Arc Length Parametric

Answer 26

Question 27

Arc Length of a Polar curve

Answer 27

Question 28

Area enclosed by a polar curve

Answer 28

Question 29

Second Derivative of Parametric

Answer 29

Question 30

Acceleration Vector

Answer 30

Question 31

Speed of Parametric

Answer 31

Question 32

Total Distance Parametric

Answer 32

integral of velocity (V)

Question 33

Sum of an Infinte Geometric Series

Answer 33

Question 34

Nth term Test

Answer 34

Question 35

Geometric Series Test

Answer 35

Question 36

P-series

Answer 36

Question 37

Alternating series

Answer 37

Question 38

Alternating Series Error Bound

Answer 38

Question 39

Ratio Test

Answer 39

CHECK ENDPOINTS

Question 40

Direct Comparison

Answer 40

If bigger series C, smaller must also C If smaller series D, bigger must also D

Question 41

Limit Compairson Test

Answer 41

either both series C or D

Question 42

Absolutely Convergent

Answer 42

Question 43

Taylor Series

Answer 43

Question 44

Lagrange Error Bound

Answer 44

M for sin and cos = 1

Question 45

Elementary Function: e^x

Answer 45

Question 46

Elementary Function: cosx

Answer 46

Question 47

Elementary Function: sinx

Answer 47

Question 48

Elementary Function: 1 / (1-x)

Answer 48

Question 49

Reiman Sums

Answer 49

Question 50

Trapezoidal Sum

Answer 50