Taylor Polynomial centered at x = 4 to approximate √4.001

[tsj1114]

"Use a 2nd order Taylor polynomial centered at x = 4 to approximate √4.001.You can leave your answer as the sum or difference of fractions."

I'm a little confused on how to set up this problem and approximate a number versus a function with x. Please help! Thank you!

 

[Steven G]

"Use a 2nd order Taylor polynomial centered at x = 4 to approximate √4.001.You can leave your answer as the sum or difference of fractions."

I'm a little confused on how to set up this problem and approximate a number versus a function with x. Please help! Thank you!

The first step you need to make is to decide which function to use. Think about what number closest to 4.001 that you actually know the square root of. You should get a real number, but since I do not want to tell you that number let's call it a and say square root of a = b. Now think of a function f(x), such that f(a) = b. It is actually an obvious function. Now use the definition of the taylor polynomial to write a 2nd order T P.

Please get back to us with your work.

 

[screw]

The first step you need to make is to decide which function to use. Think about what number closest to 4.001 that you actually know the square root of. You should get a real number, but since I do not want to tell you that number let's call it a and say square root of a = b. Now think of a function f(x), such that f(a) = b. It is actually an obvious function. Now use the definition of the taylor polynomial to write a 2nd order T P.

Please get back to us with your work.

Im also having trouble with this problem. What youre saying is somewhat confusing. Is the equation supposed to be x/2? And do we use that for the taylor series?

 

[tsj1114]

Okay.. so a number close to 4.001 is 4. So square root of 4 is 2.

For a function f(x) where f(a)=b.
This is where I am still getting a little lost. I'm thinking that f(4)=2. So the function should be x/2 ?

 

[tsj1114]

The first step you need to make is to decide which function to use. Think about what number closest to 4.001 that you actually know the square root of. You should get a real number, but since I do not want to tell you that number let's call it a and say square root of a = b. Now think of a function f(x), such that f(a) = b. It is actually an obvious function. Now use the definition of the taylor polynomial to write a 2nd order T P.

Please get back to us with your work.

Okay.. so a number close to 4.001 is 4. So square root of 4 is 2.

For a function f(x) where f(a)=b.
This is where I am still getting a little lost. I'm thinking that f(4)=2. So the function should be x/2 ?

 

[ksdhart2]

Well, f(x)=x/2 certainly does satisfy the criteria that f(4)=2, that's true. But now you have to ask yourself: Would finding the 2nd order Taylor polynomial of x/2 help you solve the problem? Why or why not? If not, can you maybe think of a different function that satisfies f(4)=2? As a hint, consider exactly what you're asked to do - find the square root of 4.001.

 

[tsj1114]

Hmm.. okay so x^1/2 also satisfies f(4)=2.
This would give me 2+ (x-4)/4 - ((x-4)^2)/64....?

 

[tsj1114]

I think I'm understanding it now. So from there I'm going to make x = 4.001 and then calulate my answer.