Taylor polynom of f(x)=1/(√1-e3x)

[Susenkovykral]

Hello,

I can't find solution for Maclaurin (Taylor a=0) polynom of function: f(x)=1/(√1-e3x).

Could you help me please?
Thank you so much for help

Andrea

 

[mfb]

I think something went wrong with formatting. I guess you didn't mean$$f(x) = \frac 1 {\sqrt 1 - e3x}$$
Is this homework?

 

[Susenkovykral]

I'm sorry. I made wrong formattion. The function is in the picture http://file:///C:/Users/nemkv/Desktop/function.JPG

It is from the exams.

 

[mfb]

I moved the thread to the homework section.
$$f(x)=\sqrt{1-e^{3x}}$$
Where did you run into problems?

Edit: Fixed sign. With minus it is odd.

 

[Susenkovykral]

The function you wrote, its wrong, it is with minus, not with plus.
My problem starts whan I make first (second, third, ..)derivation of this function and then I change x=a, and decide a=0.
When I decided a=0 the denominator equals 0. And I can't divide by zero. So I have no results.

 

[Ray Vickson]

The function you wrote, its wrong, it is with minus, not with plus.
My problem starts whan I make first (second, third, ..)derivation of this function and then I change x=a, and decide a=0.
When I decided a=0 the denominator equals 0. And I can't divide by zero. So I have no results.

The function you wrote, its wrong, it is with minus, not with plus.
My problem starts whan I make first (second, third, ..)derivation of this function and then I change x=a, and decide a=0.
When I decided a=0 the denominator equals 0. And I can't divide by zero. So I have no results.

The function $f(x) = \sqrt{1-e^{3x}}$ does not have a series expansion in powers of $x-a$ when $a = 0$ (that is, a Maclauren expansion). The function $f(x)$ is real when $x < 0$ but is pure imaginary when $x > 0$, and there is no way any function like that can have a Maclauren expansion.

This is either a "trick" question or else you copied it incorrectly.

 

[Susenkovykral]

Thank you so much. I have checked the function and I have copied it correctly. So It really looks like a trick.

Thanks for your time.
Best regard

Andrea