Compute T4(x) of cos x centered at a = 0 and use a calculator to compute the err

Question

Compute T4(x) of cos x centered at a = 0 and use a calculator to compute the error |f(x) - T4| at x = pi/2 so i computed t_4(x) = 1-1/2x^2+1/24x^4 This is correct. I just don't know how to compute the error. For one I'm not sure if this is even the right formula: |f(x) - Tn(x)| =< ( K * |x-a|^(n+1))/(n+1)! and what is my K? is it what the graph of my 5th derivative : -sin(x) bounded by in the interval a to x? If so it would be -1, but then if i have my K, then what am I solving the inequality for??? any help would be appreciated, I don't really care what the answer is, well obviously I do a bit, I just want to know how to execute it to find the error. so please show steps, or at least explain what steps are.. thanks!

Explanation / Answer

We know that the Taylor Series for cos(x) centered at a = 0 is: cos(x) = ? [(-1)^n * x^(2n)]/(2n)! (from n=0 to infinity). So T4(x) is this summation from n=0 to 2. So: T4(x) = ? [(-1)^n * x^(2n)]/(2n)! (from n=0 to 2) = 1 - (1/2)x² + (1/24)x4. So we see that: T4(p/7) = 1 - (1/2)(p/7)² + (1/24)(p/7)4 ˜ 0.90098. cos(p/7) ˜ 0.90097. Thus, |cos(p/7) - T4(p/7)| = 0.00001.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.