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I don't understand how to determine the accuracy order of different numerical methods

I have two examples:

(1)

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(2)

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For the (1) I get that the quotient for the errors are $16$ and for (2) I get that the quotient is $4$. And from what my teacher says, knowing that the quotient is $4$ then, $2^2=4$ and so the accuracy order is $2$. So I assumed that the same goes for ex. (1) so $2^4=16$ so the accuracy order should be $4$, but the correct answer is $1$ which I don't understand.

Could someone please explain how to determine the accuracy order from the given data. Thank you!

katara
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    I agree your argument. Is $1$ the result given in the book ? – Peter Mar 12 '20 at 17:40
  • @Peter This is an exam question and in the answer key it says: "quadrature with accuracy order 1. The error decreases linearly with h" – katara Mar 12 '20 at 20:06

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