# How do you use Newton's method to find the approximate solution to the equation #x+1/sqrtx=3#?

Newton's method (or the Newton-Raphson method) entails:

Then, taking the derivative gives the general form:

So, if you write this in your TI-83+ calculator:

which actually looks like this:

Check the solution:

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To use Newton's method to find the approximate solution to the equation ( x + \frac{1}{\sqrt{x}} = 3 ), follow these steps:

- Start with an initial guess for the solution, ( x_0 ).
- Use the formula: [ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} ] where ( f(x) ) is the given equation and ( f'(x) ) is its derivative.
- Repeat this process iteratively until the value of ( x ) converges to the desired accuracy.

In this specific equation, ( f(x) = x + \frac{1}{\sqrt{x}} - 3 ). To find ( f'(x) ), differentiate ( f(x) ) with respect to ( x ): [ f'(x) = 1 - \frac{1}{2x^{3/2}} ]

Now, choose an initial guess ( x_0 ) and use the formula to iteratively approximate the solution until convergence is achieved.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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