Lagrange Error Bound for Taylor Polynomials - AP Calculus BC
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Let 
be the fifth-degree Taylor polynomial approximation for 
, centered at 
.
What is the Lagrange error of the polynomial approximation to 
?
Let
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 
The fifth degree Taylor polynomial approximating
The Lagrange error is the absolute value of the next term in the sequence, which is equal to
We need only evaluate this at
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Let be the fifth-degree Taylor polynomial approximation for , centered at .
What is the Lagrange error of the polynomial approximation to ?
Let
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
The fifth degree Taylor polynomial approximating
The Lagrange error is the absolute value of the next term in the sequence, which is equal to
We need only evaluate this at
Compare your answer with the correct one above