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# Use Newton's method with the specified initial approximation $x_1$ to find $x_3$, the third approximation to the root of the given equation. (Give your answer to four decimal places.)$\dfrac{2}{x} - x^2 + 1 = 0$, $x_1 = 2$

## $$x_{3} \approx 1.5215$$

Derivatives

Differentiation

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

the first thing you can do is differentiate the equation we've been given, which gives us negative to overact squared minus two acts. Okay, now that we've got that, we know that when acts is two, we have 1.55 because we're using the formula Axe Marchioness to over acts minus X squared plus one divided by negative to over X squared minus two acts. Therefore, when X is 1.55 we have acts over here would be 1.5215

#### Topics

Derivatives

Differentiation

Volume

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp