Lagrange Error Bound for Taylor Polynomials Flashcards - AP Calculus BC

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

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Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

Question

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Answer

The fifth degree Taylor polynomial approximating centered at is:

$sin(x) \approx x - \frac{x^3}{3!} + \frac{x^5}{5!}$

The Lagrange error is the absolute value of the next term in the sequence, which is equal to $\left |\frac{x^7}{7!} \right |$ .

We need only evaluate this at and thus we obtain $\frac{1^7}{7!} = \frac{1}{7!}$

Compare your answer with the correct one above

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Lagrange Error Bound for Taylor Polynomials - AP Calculus BC

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let be the fifth-degree Taylor polynomial approximation for , centered at . What is the Lagrange error of the polynomial approximation to ?

The fifth degree Taylor polynomial approximating centered at is: The Lagrange error is the absolute value of the next term in the sequence, which is equal to . We need only evaluate this at and thus we obtain

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Let $P_{5}(x)$ be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?