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Unformatted text preview: Math1011 Section 2.4 9/16/2009 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. ƒ (2) = 4 ƒ (1) = 0 ƒ (0) does not exist ( ) 2 lim x f x → = − 2 ( ) 2 lim x f x → − = − 1 ( ) lim x f x → = 9/16/2009 Math1011 Section 2.4 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. ƒ (2) = 4 ƒ (1) = 0 ƒ (0) DNE ( ) 2 lim x f x → = − 2 ( ) 2 lim x f x → − = − 1 ( ) lim x f x → = Note: This is one of many (infinite) correct answers. Your graph may look quite different from the above graph, and still be absolutely correct. (Doc #011w.24.01t) Math1011 Section 2.4 2 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. ƒ (0) does not exist 1 ( ) 2 lim x f x → = − 2 ( ) 1 lim x f x →− − = − 2 ( ) lim x f x DNE →− = 4 ( ) lim x f x → = ƒ (2) = 1 ƒ (1) = 3 ƒ (4) = 4 2 Math1011 Section 2.4 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. ƒ (0) does not exist 1 ( ) 2 lim x f x → = − 2 ( ) 1 lim x f x →− − = − 2 ( ) lim x f x DNE →− = 4 ( ) lim x f x → = ƒ (2) = 1 ƒ (1) = 3 ƒ (4) = 4 Note: This is one of many (infinite) correct answers. Your graph may look quite different from the above graph, and still be absolutely correct. (Doc #011w.24.02t) Math1011 Section 2.4 3 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. 1 lim ( ) lim ( ) lim ( ) 2 lim ( ) lim ( ) 1 x x x x x f x f x f x f x f x → → → ∞ → − → −∞ = −∞ = ∞ = = = + −∞ Math1011 Section 2.4 3 Sketch the graph of an example of a function ƒ that satisfies all of the given conditions. 1 lim ( ) lim ( ) lim ( ) 2 lim ( ) lim ( ) 1 x x x x x f x f x f x f x f x → → → ∞ → − → −∞ = −∞ = ∞ = = = + −∞ Note: This is one of infinitely many correct answers. Your graph may look quite different from the above graph, and still be absolutely correct. (Doc #011w.24.03t) Math1011 Section 2.4 4 Find the limit 1 lim x x → − 1 lim x x → + 1 lim x x → 1 lim x x → ∞ 1 lim x x → −∞ What are the horizontal and vertical asymptotes of 1/x? Math1011 Section 2.4 4 Find the limit 1 lim x x → − = −∞ As x goes to 0 from the left, 1/x gets small: 1/1 = 1, 1/.1 = 10, 1/.01 = 100, etc....
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