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### 42 Cards in this Set

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 Finding inverse of a function 1.) determine if function is one-to-one, consider domain 2.) write y in place of f(x) 3.) solve for x 4.) exchange x and y, consider domain 5.) replace y with f-1(x) d/dx sin x cos x d/dx cos x -sin x d/dx tan x sec² x d/dx csc x -csc x cot x d/dx sec x sec x tan x d/dx cot x -csc² x lim e^x x->∞ ∞ lim e^x x->-∞ 0 lim e^x-1/x x->0 1 eº = 1 e¹ = e ln e = 1 ln 1 = 0 ln e³ = 3 change of base formula this equals this ∫ xⁿ dx (x^(n + 1) / n + 1) + C ∫ e^x dx e^x + C ∫ sin x dx -cos x + C ∫ sec² x dx tan x + C ∫ sec x tan x dx sec x + C ∫ sinh x dx cosh x + C ∫ tan x dx ln |sec x| + C ∫ 1 / x dx ln |x| + C ∫ a ^x dx (a^x / ln a) + C ∫ cos x dx sin x + C Theorem 7 differentiating inverse functions 1 / f'(f^-1) Find inverse value and plug into differentiated formula d/dx (ln |x|) 1 / x d/dx (arcsin x) 1 / √(1 - x²) -1 < x < 1 d/dx (arccos x) -[ 1 / √(1 - x²) ] -1 < x < 1 d/dx (arctan x) 1 / 1 + x² d/dx (csc^-1 x) -[ 1 / (x)√(x² - 1) ] d/dx (sec^-1 x) 1 / (x)√(x² - 1) d/dx (cot^-1 x) -[ 1 / 1 + x² ] d/dx log base a (x) 1 / x ln(a) d/dx a^x a^x ln(a) lim x->0 (1 + x)^1/x e arcsin(sin x) x for -π/2 ≦ x ≦ π/2 sin (arcsin x) x for -1 ≦ x ≦ 1 arccos(cos x) x for 0 ≦ x ≦ π cos (arccos x) x for -1 ≦ x ≦ 1