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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: