Section 2.3 Part One

# Section 2.3 Part One - The functions which have the Direct...

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Section 2.3: Evaluating Limits Analytically (Algebraically) Basic Limits: For b and c real valued constants: lim x c b b = lim x c x c = lim n n x c x c = Properties of Limits: (These properties apply to all limits) Let ( ) ( ) lim and lim x c x c f x L g x M = = : ( ) ( ) lim lim x c x c bf x b f x bL = = ( ) ( ) ( ) ( ) lim lim lim x c x c x c f x g x f x g x L M ± = ± = ± ( ) ( ) ( ) ( ) lim lim lim x c x c x c f x g x f x g x LM = = ( ) ( ) ( ) ( ) lim lim , 0 lim x c x c x c f x f x L M g x g x M = = ( ) ( ) lim lim n n n x c x c f x f x L = = Direct Substitution Property: A function f has the direct substitution property if: ( ) ( ) lim x c f x f c = A function has the direct substitution property unless it doesn’t.

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Unformatted text preview: The functions which have the Direct Substitution Property everywhere in their domains are: Function Domain Polynomials ( ) ,-∞ ∞ Rational Functions ( ) ( ) ( ) ( ) { } f x h x : x | g x g x = ≠ Radical Functions ( ) ( ) n n even [0, ) f x x n odd , ∞ = = -∞ ∞ Transcendental Functions -Trigonometric ( ) ( ) ( ) f x sin x or cos x : , n f x tan x :x , n odd 2 π =-∞ ∞ = ≠-Logarithmic ( ) ( ) a f x ln x or log x : 0, = ∞-Exponential ( ) ( ) ( ) x x f x e or a a 0 : , = ≠-∞ ∞ Composite Functions...
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Section 2.3 Part One - The functions which have the Direct...

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