Solve the Problem $f ( x ) = \sqrt [ a ] { x } , a > 0$

question 242

Essay

Solve the problem.
-Apply Newton's method to $f ( x ) = \sqrt [ a ] { x } , a > 0$ , and write an expression for $x _ { n } + 1$ . If the initial guess $x _ { 0 }$ is greater than or equal to 1 , what happens to $\left| x _ { n } + 1 \right|$ as $n \rightarrow \infty$ ?

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Definitions:

Bryophytes

Term used to identify plants that do not have vascular tissue. Includes the liverworts, hornworts, and mosses.

Vascular Tissue

The complex tissue in plants responsible for conducting water, minerals, and nutrients throughout the plant.

Ferns

are a group of plant species that reproduce via spores and have neither seeds nor flowers, characterized by large, divided leaves.

Megaspore

A type of spore that is larger in size, produced by certain plants, that develops into a female gametophyte.