Question

30-4b65-8a8e-742ad3984061/Announcements/045e1838-5fc2-48f2-be7 ... YouTube Maps LimeTorrents 2020 \( -\ldots \) (2) Lessons from th... (iii) Show that the approximate value of \( \sqrt[4]{17} \) is 2.03125 . (iv) Show that the approximate value of 2.03125 is only correct up to 2 decimal places. That is, we can only say with certainty, \( \sqrt[4]{17}=2.03 \). 2. TAYLOR POLYNOMIALS Question 2. [2, 6,1, 5 marks] Use the second order Taylor polynomial about 16 to approximate \( \sqrt[4]{17} \), as follows: (i) Explain why the tabular point \( x_{0}=16 \) is a good tabular point. (ii) Prove the the replacement cubic at \( x_{0}=16 \) is given by \[ P_{3}(x)=2+\frac{1}{2^{5}}(x-16)-\frac{3}{2^{12}}(x-16)^{2}+\frac{21}{3 \cdot 2^{18}}(x-16)^{3} . \] (iii) Show that the approximate value of \( \sqrt[4]{17} \) is \( 2.03054428100585 \ldots \) (iv) Show that the approximate value of \( 2.03054428100585 \ldots \) is only correct up to 4 decimal places. That is, we can only say with certainty, \( \sqrt[4]{17}=2.0305 \).

          30-4b65-8a8e-742ad3984061/Announcements/045e1838-5fc2-48f2-be7 ...
YouTube
Maps
LimeTorrents 2020
\( -\ldots \)
(2) Lessons from th...
(iii) Show that the approximate value of \( \sqrt[4]{17} \) is 2.03125 .
(iv) Show that the approximate value of 2.03125 is only correct up to 2 decimal places.

That is, we can only say with certainty, \( \sqrt[4]{17}=2.03 \).
2. TAYLOR POLYNOMIALS

Question 2. [2, 6,1, 5 marks] Use the second order Taylor polynomial about 16 to approximate \( \sqrt[4]{17} \), as follows:
(i) Explain why the tabular point \( x_{0}=16 \) is a good tabular point.
(ii) Prove the the replacement cubic at \( x_{0}=16 \) is given by
\[
P_{3}(x)=2+\frac{1}{2^{5}}(x-16)-\frac{3}{2^{12}}(x-16)^{2}+\frac{21}{3 \cdot 2^{18}}(x-16)^{3} .
\]
(iii) Show that the approximate value of \( \sqrt[4]{17} \) is \( 2.03054428100585 \ldots \)
(iv) Show that the approximate value of \( 2.03054428100585 \ldots \) is only correct up to 4 decimal places.

That is, we can only say with certainty, \( \sqrt[4]{17}=2.0305 \).

30-4b65-8a8e-742ad3984061/Announcements/045e1838-5fc2-48f2-be7 ...
YouTube
Maps
LimeTorrents 2020
-…
(2) Lessons from th...
(iii) Show that the approximate value of √(17) is 2.03125 .
(iv) Show that the approximate value of 2.03125 is only correct up to 2 decimal places.

That is, we can only say with certainty, √(17)=2.03.
2. TAYLOR POLYNOMIALS

Question 2. [2, 6,1, 5 marks] Use the second order Taylor polynomial about 16 to approximate √(17), as follows:
(i) Explain why the tabular point x0=16 is a good tabular point.
(ii) Prove the the replacement cubic at x0=16 is given by

P3(x)=2+(1)/(2^5)(x-16)-(3)/(2^12)(x-16)^2+(21)/(3 · 2^18)(x-16)^3 .

(iii) Show that the approximate value of √(17) is 2.03054428100585 …
(iv) Show that the approximate value of 2.03054428100585 … is only correct up to 4 decimal places.

That is, we can only say with certainty, √(17)=2.0305.

Added by Juan Carlos T.

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