P 5 ( x ) = + x + x 2 + x 3 + x 4 + x P 5 ( x ) = + ( x ? 1/4) + ( x ? 1/4) 2 +

Question

P5(x) = + x + x2 + x3 + x4 + x

P5(x) = + (x ? 1/4) + (x ? 1/4)2 + (x ? 1/4)3 + (x ? 1/4)4+(x ? 1/4)5

P5(x) = + (x ? 1) + (x ? 1)2 + (x ? 1)3 + (x ? 1)4 +(x ? 1)5

1-Find the fifth Maclaurin polynomial for f(x) = x e4x.

P5(x) = + x + x2 + x3 + x4 + x

2-Find the fifth Taylor polynomial for f(x) = x ln(4x), expanded about c = 1/4.

P5(x) = + (x ? 1/4) + (x ? 1/4)2 + (x ? 1/4)3 + (x ? 1/4)4+(x ? 1/4)5

3-Find the fifth Taylor polynomial for f(x) = x5 ? 5x4 + x3 + x2 + 5x + 1, expanded about c = 1.

P5(x) = + (x ? 1) + (x ? 1)2 + (x ? 1)3 + (x ? 1)4 +(x ? 1)5

Explanation / Answer

1)

P5(x) = 0 + 1*x + 4*x^2 + 8x^3 + (32/3)x^4 + (32/3)x^5

2)

P5(x) = 0 + 1*(x-1/4) + 2*(x-1/4)^2 - (8/3)(x-1/4)^3 +(16/3)(x-1/4)^4 - (64/5)(x-1/4)^5

3)

P5(x) = 4-5(x-1)-16(x-1)^2-9(x-1)^3 + 0(x-1)^4 + 1*(x-1)^5

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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