Question

Consider the equation x^2=e^2+2.
Sarting with x1=-1, apply interation of new tons method to compute approximate solutions x2

Answer 1

so all i have to do is to derivative the equation?

Answer 2

then x1-(f(x)/(f(x)

Answer 3

it is really
\[x^2=e^2+2\]?

Answer 4

No sorry,
its
x^2=e^x+2

Answer 5

that is what i though
start with
\[f(x)=e^x-x^2+2\] and then \(f'(x)=e^x-2x\)

Answer 6

then
\[x_2=-1-\frac{f(-1)}{f'(-1)}\] and probably a calculator

Answer 7

did you drivative?

Answer 8

Hmm I don't see the need of using integration here, you can straight away approximate x from
\[\large x^2=e^x+3 \\ \\ \large x_{n+1}=\pm \sqrt{e^{x_n}+3}\]
Then use -1 for \(+\sqrt{...} ~~~and~~~-\sqrt{...}\) See if which gives you a constant value throughout the calcs

Answer 9

so i do not need to drivitative the equation?

Answer 10

Yeah try it out you should get some recurring numbers

Answer 11

sorry the proper equation is
x^2=e^x+2 @.Sam.

Answer 12

Oh doesn't matter, change the 3 to 2

Answer 13

\[\large x^2=e^x+2 \\ \\ \large x_{n+1}=\pm \sqrt{e^{x_n}+2}\]
Iterate when x=-1