formula sheet

MATH 110B FORMULA SHEET

LIMIT OF A FUNCTION

DEFINITION OF THE DERIVATIVE

DERIVATIVES OF POLYNOMIALS

DERIVATIVE OF A PRODUCT

DERIVATIVE OF A QUOTIENT

DERIVATIVE OF A POWER

CHAIN RULE

DERIVATIVE OF A POWER OF y

THREE APPROXIMATE DERIVATIVES

Forward

Backward

Central

USEFUL TRIGONOMETRIC IDENTITIES

DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS

If u is a function of x, then for:

INDICES

LOGARITHMIC RULES

DIFFERENTIATION OF LOGARITHMIC FUNCTIONS

If u is a function of x, then for:

DIFFERENTIATION OF EXPONENTIAL FUNCTIONS

If u is a function of x, then for:

COMPLETING THE SQUARE

Given the quadratic expression:

Completing the square:

NUMERICAL INTEGRATION FORMULAE(a) The Mid-point or Rectangle rule

Where and are the mid-points of the n rectangles

(b) The Trapezoidal rule

Where

(c) Simpson’s rule

Where and n must be even

Error = Actual value – Obtained value

% Error =

INDEFINITE INTEGRALINTEGRALS

INTEGRATION BY PARTS

TABLE OF TRIGONOMETRIC SUBSTITUTION

Expression Substitution Identity

OR

INTEGRATION OF TRIGONOMETRIC FUNCTIONS

Vector differential calculus

Directional Derivative

INTEGRATION OF INVERSE TRIGONOMETRIC FUNCTIONS

Series Expansions

Maclaurin’s Series:

Taylor’s Series:

OR

Differential Equations

Integrating Combinations

For the first-order linear differential equation: