AP Calculus BC : Lagrange Error Bound for Taylor Polynomials

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

Example Question #1 : Lagrange's Theorem

Let  be the fifth-degree Taylor polynomial approximation for , centered at .

What is the Lagrange error of the polynomial approximation to ?

Possible Answers:

Correct answer:


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 

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