# 3. Consider the sequence (x,) with x, =3 defined recursively by the ruleX 4-x Explore the...

###### Question:

3. Consider the sequence (x,) with x, =3 defined recursively by the ruleX 4-x Explore the sequence with your calculator: a. 1 STO X STO 3-X ENTER, ENTER ENTER ENTER. 4-x Apparently the sequence diverges / converges to b. State the MONOTONE CONVERGENCE THEOREM: c. Use induction to show that (x) is decreasing for all n when x, 3 d. Use induction to show that (x.) is bounded below by 0 when x,- 3. e. Conclude from (b-d): d. To find the limiting value L, realize that lim x, lim x=L Then use the recursion to find the value of L.

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