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The function f in the given figure satisfies lim f(x) = 5. For each value of e, find all values of X-2 8>0 such that f(x)-5| <& whenever 0 < x-2|<8. (a) ε =2 (b) e = 1 (c) For any e, make a conjecture about the corresponding value of 8 satisfying the above description. (a) When & = 2, the values of 8 >0 such that f(x)-5| 0 such that f(x)-5| 0, make a conjecture that the values of 8>0 such that |f(x) - 5|

The function f in the given figure satisfies lim f(x) = 5. For each value of e, find all values of X-2 8>0 such that f(x)-5| <& whenever 0 < x-2|<8. (a) ε =2 (b) e = 1 (c) For any e, make a conjecture about the corresponding value of 8 satisfying the above description. (a) When & = 2, the values of 8 >0 such that f(x)-5| 0 such that f(x)-5| 0, make a conjecture that the values of 8>0 such that |f(x) - 5|

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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K The function f in the given figure satisfies lim f(x) = 5. For each value of e, find all values of X→2 8>0 such that f(x)-5| <& whenever 0 < x-2<8. (a) ε =2 (b) ε = 1 (c) For any e, make a conjecture about the corresponding value of 8 satisfying the above description. C (a) When & = 2, the values of 8>0 such that f(x)-5| <e whenever 0 < x-2 <8 satisfy the inequality. (Type an inequality using 8 as the variable. Simplify your answer.) (b) When & = 1, the values of 8>0 such that f(x)-5| <e whenever 0 < x-2<8 satisfy the inequality. (Type an inequality using 8 as the variable. Simplify your answer.) (c) From parts (a) and (b), for any e > 0, make a conjecture that the values of 8>0 such that f(x) - 5 <e whenever 0 < x-2| <8 satisfy the inequality. (Type an inequality using 8 and e as the variables. Simplify your answer.) 20+ 18- 16- 14 12- 10- 8- 6- 4 2+ 0- 0 2 4 6 X 8 10 12 14 16 18 20 Q Q
Transcribed Image Text:K The function f in the given figure satisfies lim f(x) = 5. For each value of e, find all values of X→2 8>0 such that f(x)-5| <& whenever 0 < x-2<8. (a) ε =2 (b) ε = 1 (c) For any e, make a conjecture about the corresponding value of 8 satisfying the above description. C (a) When & = 2, the values of 8>0 such that f(x)-5| <e whenever 0 < x-2 <8 satisfy the inequality. (Type an inequality using 8 as the variable. Simplify your answer.) (b) When & = 1, the values of 8>0 such that f(x)-5| <e whenever 0 < x-2<8 satisfy the inequality. (Type an inequality using 8 as the variable. Simplify your answer.) (c) From parts (a) and (b), for any e > 0, make a conjecture that the values of 8>0 such that f(x) - 5 <e whenever 0 < x-2| <8 satisfy the inequality. (Type an inequality using 8 and e as the variables. Simplify your answer.) 20+ 18- 16- 14 12- 10- 8- 6- 4 2+ 0- 0 2 4 6 X 8 10 12 14 16 18 20 Q Q
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