How do you define iterations of multivariable functions?

To be clear(example):

If \(\displaystyle{f}:\mathbb{R}^{{2}}\rightarrow\mathbb{R}\)

How do you define

\(\displaystyle{f}\circ{f},\text{or}{f}\circ\ldots\circ{f}?\)?

Your answer

asked 2022-01-04

To be clear(example):

If \(\displaystyle{f}:\mathbb{R}^{{2}}\rightarrow\mathbb{R}\)

How do you define

\(\displaystyle{f}\circ{f},\text{or}{f}\circ\ldots\circ{f}?\)?

asked 2021-12-18

Find the linear approximation of the function \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{4}-{x}}}\) at \(\displaystyle{a}={0}\) and use it to approximate the numbers \(\displaystyle\sqrt{{{3.9}}}\) and \(\displaystyle\sqrt{{{3.99}}}\), please.

asked 2021-10-14

Part A: Find the local linear approximation of the function \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{3}+{x}}}\ \text{ at }\ {x}_{{0}}={6}\),

Part B use part A to approximate \(\displaystyle\sqrt{{{8.9}}}\ \text{ as }\ \sqrt{{{9.1}}}\). Answers must be in fractions

Part B use part A to approximate \(\displaystyle\sqrt{{{8.9}}}\ \text{ as }\ \sqrt{{{9.1}}}\). Answers must be in fractions

asked 2021-08-11

Find the linear approximation of the function \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{1}-{x}}}\) at a=0 and use it to approximate the numbers \(\displaystyle\sqrt{{{0.9}}}\) and \(\displaystyle\sqrt{{{0.99}}}\).

asked 2021-08-20

Find the linear approximation of the function \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{4}-{x}}}\) at a=0

Use L(x) to approximate the numbers sqrt (3.9) and sqrt (3.99) Round to four decimal places

Use L(x) to approximate the numbers sqrt (3.9) and sqrt (3.99) Round to four decimal places

asked 2021-05-03

Find the linear approximation of the function \(f(x) = \sqrt{1-x}\) at a = 0 and use it to approximate the numbers \(\sqrt{0.9}\) and \(\sqrt{0.99}\). (Round your answers to four decimal places.)

L(x) =

\(\sqrt{0.9} \approx\)

\(\sqrt{0.99} \approx\)

L(x) =

\(\sqrt{0.9} \approx\)

\(\sqrt{0.99} \approx\)