Math 9C Sec 4.4

# Math 9C Sec 4.4 - Example Find the horizontal and vertical...

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Math 9A Section 4.4 Limit Set Infinity Definition: Let f be a function defined on some interval (a, ∞) lim →∞ = x fx L if the values of f(x) can be made arbitrarily close to L by taking x to be sufficiently large. Definition: The limit y=L is a HORIZONTAL ASYMPTOTE of f(x) if either lim →∞ = x fx L or lim →-∞ = x fx L . Theorem: If r 0 is rational, then ˃ lim →∞ = x 1xr 0 . If r 0 is rational such that ˃ xr is defined for all x, then lim →-∞ = x 1xr 0 . Example: lim →∞ - - + + = - - + + = - - + + = x 3x2 x 25x2 4x 1x2x2 3 1x 2x25 4x 1x2 3 0 05 0 0 35

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Unformatted text preview: Example: Find the horizontal and vertical asymptotes of f(x)= +-2x2 13x 5 . VA: 3x-5=0 x= 53 HA: lim →∞ x +-2x2 13x 5 = lim →∞ x + ( -) x2 1x2x 3 5x = lim →∞ x + ( -) 2 1x2 3 5x = lim →∞ x 23 Example: f(x)= + x2x2 3 _________________O__________________ f’(x)= ( + ) 6x x2 3 2 x=0-1 1 f’’(x)= ( -)( + ) 18 1 x2 x2 3 3 =0 ____________O_________O_____________ x= ± 1 Critical Number: x=0 Point of Inflection: x= ± 1...
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## This note was uploaded on 06/23/2010 for the course MATH 9A taught by Professor Apoorva during the Spring '07 term at UC Riverside.

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Math 9C Sec 4.4 - Example Find the horizontal and vertical...

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