Taylor Polynomial

The answer in third-degree Taylor polynomial for f(x)=ln x, centered at a = 2 is ln(2) + ½(x+2) – 1/8(x-2)² + 1/24(x-2)³.

• true

• false

What is the second derivative for finding the nth Taylor polynomial of y= In x at x=1?

• -2

• 2

• -1

• 1

Which of the following gives the Taylor polynomial of order three of the function f(x) = sin x at a = π/2?

• a.) 1- (x- π/2) ²/ 2!

• b.) –(x-π/2) + (x-π/2) ³/3!

• c.) (x-π/2) -(x-π/2) ³

• d.) (x+π/2) + (x-π/2) ²

17. Write out the general formula for the fourth degree Taylor Polynomial of a function f (x) at a. The following is the fourth-order Taylor Polynomial of a function f(x) at a =3. What is f(²) (3)?

• a.) 5

• b.) 6π

• c.) 20

• d.) 3

The following is the fifth order Taylor Polynomial of the function f(x) at a T5(x) = 2-2(x-a) +√5(x-a) ²-π/2(x-a) ³+(x-a) ⁴+13(x-a) ⁵. What is f(³)(a)?

• a.) 2√5

• b.) -3π

• c.) -π/2

• d.) √5

Which of the following is the third Taylor Polynomial of the function f(x) = sin (x/2) centered at a = π?

• (x-π) – (x-π) ³/3!

• 1- (x-π/2) ²/4(2!)

• 1- x²/4(2!)

• 1- (x-π) ²/4(2!)

The following is the fourth order Taylor Polynomial of the function f(x) at a. T4(x) = 10+5(x-a) + √3(x a) ² + 1/2π(x-a) ³ + 17e(x-a) ⁴. What is f’’’(a)?

• a.) 3/π

• b.) 2√3

• c.) 17e

• d.) 1/2π

Find the cubic approximate for f(x) = sin x at x = 3π/2 = a

• Sin x = -1 - ½ (x - 3π/2)²

• Sin x = -1 + ½ (x - 3π/2)²

• Sin x = 1 - ½ (x + 3π/2)²

• Sin x = -1 - ½ (x + 3π/2)²

Use the second-degree polynomial to approximate the function 𝑓(𝑥)=2 + x + x² at the point a=1.

• 4 + 3/2 (x-1) + (x-1)²

• 4 + 3/2 (1-x) + 2/3 (1-x)²

• 4 + 3 (x-1) + (x-1)²

• 4 + 3 (x-1) + 2(x-1)²

What is the first derivative in finding the degree 4 Taylor polynomial, P₄(x), for = √x at x = 4?

• a.       1/4

• b.       1/2

• c.       1

• d.       2