Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x_0 f(x)=x^5+4x^2+3x+1, x_0 =0

Greyson Landry 2022-07-30 Answered
Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x 0 .
f ( x ) = x 5 + 4 x 2 + 3 x + 1 , x 0 = 0
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

edgarovhg
Answered 2022-07-31 Author has 12 answers
f(0) = 1
f ( x ) = 5 x 4 + 8 x + 3
f'(0) = 3
f ( x ) = 20 x 3 + 8
f'''(0) = 8
f 3 ( x ) = 60 x 2
f 3 ( 0 ) = 0
f 4 ( x ) = 120 x , f 4 ( 0 ) = 0
f 5 ( x ) = 120 , f 5 ( 0 ) = 0
so we have:
f ( x ) = 1 + 3 1 ! x + 8 2 ! x 2 + 0 3 ! x 3 + 0 4 ! x 0 + 120 5 ! x 5 = 1 + 3 x + 4 x 2 + x 5
since we only consider n=4, we have:
f ( x ) = 1 + 3 x + 4 x 2
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions