Numerical Methods : Function Evaluations, Real & Complex Zeros

Study concepts, example questions & explanations for Numerical Methods

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Example Questions

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

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

 

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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 #6 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

 

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

 

Possible Answers:

Correct answer:

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 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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 #10 : Function Evaluations, Real & Complex Zeros

Use Newton's method to determine  for  if .

Possible Answers:

Correct answer:

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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