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Standard forms; Standard substitutions; Integration by parts; Differentiation of an integral;. Dirac ?-'function'; Reduction formulae. 11. equation; Spherical harmonics. 12. Calculus of Variations. integration of differential equations;. Central difference notation; Approximating to derivatives; Interpolation: Everett's formula;.
DIFFERENTIAL AND INTEGRAL. CALCULUS. WITH EXAMPLES AND APPLICATIONS. BY. GEORGE A. OSBORNE, S.B.. WALKER PROFESSOR OF MATHEMATICS IN THE MASSACHUSETTS. INSTITUTE OF in Chapter X. of the Differential Calculus, on Maxima and Minima, . Equation of Tangent Planes. Angle with
Tir estiuratc the slope of a gralrh at a poirrt rha,n a trrngerrt lirx-'to tltc graph at tliat point. Arrother rva. is (lx' using u grtrphit s cak'nla,tor') to "zoonr in" aroLtn<l the point itt cluestiorr urrtil the glaph "kroks'' straight.'fhis rrretliocl alnrost ahva'"s il)r'ks. If u'c' "zot.rttt in" att<l ther glaph Lr,rks stlaiglrt at a point. sa)'.r': o. then the
DIFFERENTIAL CALCULUS. CHAPTER I. COLLECTION OF FORMULAS. 1. Formulas for reference. For the convenience of the student we give the following list of elementary formulas from Algebra, Geome- try, Trigonometry, and Analytic Geometry. 1. Binomial Theorem (n being a positive integer): n (n ? 1) n (n ? 1) (n ? 2).
Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(x)g (x) + g(x)f (x) (4) d dx. (f(x) g(x). ) = g(x)f (x) ? f(x)g (x). [g(x)]. 2. (5) d dx f(g(x)) = f (g(x)) · g (x). (6) d dx xn = nxn?1. (7) d dx sin x = cos x. (8) d dx cos x = ? sin x. (9) d dx tan x = sec2 x. (10) d dx cot x = ? csc2 x.
Note that all but the first one of these tend to be taught in a Calculus II class. u Substitution. Given. ( ). (. ) ( ) b a. f g x g x dx. ?. ? then the substitution. ( ). u g x. = will convert this into the integral,. ( ). (. ) ( ). ( ). ( ). ( ) b. g b a. g a. f g x g x dx. f u du. ?. = ?. ? . Integration by Parts. The standard formulas for integration by parts
Revenue Function. Cost Function. Profit Function. The low prices required to. The total cost to produce. The break-even point occurs sell more units eventually units includes the fixed when result in a decreasing cost. revenue. R. C. x. Maximum profit x. Negative of fixed cost. Break-even point. P x. Fixed cost. C. Inelastic.
Elementary Differential and Integral Calculus. FORMULA SHEET. Exponents xa · xb = xa+b, ax · bx = (ab)x, (xa)b = xab, x0 = 1. Logarithms lnxy = lnx + lny, lnxa = alnx, ln 1 = 0, eln x = x, ln ey = y, ax = ex ln a. Trigonometry cos 0 = sin ?. 2. = 1, sin 0 = cos ?. 2= 0, cos2 ? + sin2 ? = 1, cos(??) = cos?, sin(??)=? sin ?, cos(A + B)
Integral Calculus Formula Sheet. Derivative Rules: ( ) 0 d c dx. = ( ). 1 n n d x nx dx. -. = (. ) sin cos d x x dx. = (. ) sec sec tan d x x x dx. = (. ) 2 tan sec d x x dx. = (. ) cos sin d x x dx. = -. (. ) csc csc cot d x x x dx. = -. (. ) 2 cot csc d x x dx. = -. ( ) ln x x d a a a dx. = ( )x x d e e dx. = ( ). (. ) ( ). (. ) d d cf x c. f x dx dx. = ( ). ( ).
Differential calculus-Outlines. What is Differential Calculus – An Introduction. Derivative or Deferential Coefficient (First Principal Definition). Basic Formulas. Laws for Differentiation (Algebra of Derivative of Functions). Derivative of A Function of Function (Chain Rule) .Derivative of Implicit Function .Derivative of Function In

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March 2018