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cos(2θ) = cos2 θ − sin2 θ = 2cos2 θ − 1 = 1 − 2sin2 θ. the midpoint, trapezoid and Simpson’s Rule and how to apply them. You will not be required to memorize the error bounds, but you should know how to use/apply the error bounds. Make sure you review ALL the questions from the homework assignments.
Sometimes we start a sequence with a0 (index zero) instead of a1. Notation: the sequence a1, a2, a3, . . . is also denoted by {an} or {an}∞ n=1. Some sequences can be defined with a formula, for instance the sequence 1, 3, 5, 7, . . . of odd positive integers can be defined with the formula an = 2n −.
However, Calculus II, or integral calculus of a single variable, is really only about two topics: integrals and series, and the need for the latter can be motivated by the former. The purpose of this rst lecture is
Calculus II : Formulas. Satya Mandal. Math 116 : Calculus II Formulas to Remember. Integration Formulas. ∫ x n dx = x n+1 / (n+1) if n+1 ≠ 0. ∫1 / x dx = ln |x|. ∫ e nx dx = e nx /n if n ≠ 0. Derivative Formulas. d/dx (x n) = nx n-1. d/dx (ln x) = 1/ x. d/dx (e mx) = me mx. Product and Quotient Rules.
CALCULUS II (Math 102) Text: Essential Calculus 2/e by James Stewart. Calculus: The study of real functions f, and their derivatives f0 and integrals R f. Let f : [a; b] ! R be continuous. De nition The de nite integral of f from a to b is. where. x. Z b Z b n X f = f(x) dx := lim f(xi) x. a n!1 i=1. = (b a)=n. and. xi = a + i x.
Calculus II Spring 2004 Chris Wendl. Final Exam: Formula Sheet. 1. Some useful antiderivatives: sec2 x dx = tan x + C. sec x dx = ln. sec x tan x dx = sec x + C. 2. Triogonometry: sec x + tan x| + C. csc2 x dx = − cot x + C. csc x dx = ln | csc x − cot x| + C. csc x cot x dx = − cscx + C.
MATH 124 – Calculus II Page 8 of 37 Aside on sigma notation and useful formulas Pn i=1 Ai is a shorthand for A1 + A2 + ··· + An. In general, anything of the form Pn i=1(···) means “plug all values of i from 1 to n in the formula (···), and sum all n terms that result.” In doing area calculations, there are some useful formulas to ...
