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classwork2 - Find δ> 0 such that if 0< | x-a |< δ...

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Classwork II Sections 2.4, 2.5 Find the solution set of | 12 - 3 x | ≥ | x | . (This is 1.8.18). Find a function f ( x ) whose graph is Graph 1 below. Sketch the graph of f ( x ) = - x if x < 0 x if 0 x < 1 1 + x if x 1 . Find the following if they exist: lim x 0 f ( x ), lim x 1 f ( x ), f (1) and lim x 1 + f ( x ). (2.4.32). Let f ( x ) = x if x is rational - x if x is irrational . Find lim x 1 f ( x ) and lim x 0 f ( x ) if possible. (2.4.37). Suppose f ( x ) takes values as in Table 1 below. What can you say about lim x . 9 f ( x ), f ( . 9), lim x 1 f ( x ) and f (1)? The function f ( x ) = x 2 has been carefully graphed, but during the night a mysterious visitor changed the values of f at a million different places. Did this affect the value of lim x a f ( x ) at any a ? Explain. (2.4.40).
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Unformatted text preview: Find δ > 0 such that if 0 < | x-a | < δ then | f ( x )-L | < ε for each of the follow-ing: • f ( x ) = x + 2 , a = 5 , L = 7 , ε = . 1 • f ( x ) = x 2-4 x + 2 , a =-2 , L =-4 , ε = . 05 • f ( x ) = x 2 + 1 , a = 1 , L = 2 , ε = . 1 A tractor wheel is to be designed with circumference within . 1 feet of 4 π feet. How close to 2 feet must the radius be? Give an ε-δ proof that lim x → 2 (2 x-3) = 1. x 3 2 1 1-1 2-2-1-3-2 x f ( x ) . 5 . 6 . 9 . 83 . 99 . 849 . 999 . 8499 1 . 001 . 8502 1 . 01 . 86 1 . 1 . 89 1 . 5 . 96 Graph 1 Table 1...
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