# Numerical Methods : Function Evaluations, Real & Complex Zeros

## Example Questions

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### Example Question #1 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 4 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 4 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #2 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 4 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 4 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #3 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 3 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 3 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #4 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 4 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 4 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #5 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 2 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 2 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #1 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 3 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 3 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #7 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 2 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 2 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #2 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 2 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 2 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #8 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 2 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 2 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

### Example Question #9 : Algorithms

Use Newton's method to determine  for  if .

Explanation:

In order to solve this problem, we need to recall newton's method.

So we need to run this equation 4 times

First let's find the derivative of

Now Newton's Method looks like.

Now plug in 4 for

Now we take this answer, and plug it back into the equation for

We keep doing this until, we get to

Below is the results of Newton's Method.

So our final answer will be

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