MediumCalculusca-250

Taylor Truncation Error Value

Problem

For f(x) = e^x, the actual truncation error of the degree-n Taylor polynomial about 0 is E = e^x - sum from k = 0 to n of x^k / k!.

Given x and n, accumulate the polynomial terms and return the difference. The result is negative for negative x once the leading omitted term dominates.

Hint

Build the partial sum term by term to avoid recomputing factorials.

Test cases

case 1

in: [1,5]

expected: 0.0016151617923787498

case 2

in: [0,10]

expected: 0

case 3

in: [2,3]

expected: 1.0557227655973174

case 4

in: [-1,4]

expected: -0.0071205588285577215

Starter codePython

def taylor_truncation_error(x, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor