Skip to content

Addresses #558 using example environment. #560

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 2 commits into from
Jan 21, 2025
Merged

Addresses #558 using example environment. #560

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
f24f7a2
Addresses #558 using example environment.
jbunn3 Jan 19, 2025
e026770
Answers go outside of statements
siwelwerd Jan 21, 2025
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
86 changes: 45 additions & 41 deletions source/calculus/source/09-PS/05.ptx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -181,12 +181,12 @@
<p>
Calculate the derivatives <m>f'(x)</m>, <m>f''(x)</m>, <m>f'''(x)</m>, and <m>f^{(4)}(x)</m>.
</p>
</statement>
<answer>
<p>
<m>f'(x)=-1/x^2</m>, <m>f''(x)=2/x^3</m>, <m>f'''(x)=-6/x^4</m>, <m>f^{(4)}(x)=24/x^5</m>
</p>
</answer>
</statement>
</task>
<task>
<statement>
Expand Down Expand Up @@ -215,25 +215,27 @@
</p>
</li>
</ol>
</statement>
<answer>
<p>
B.
</p>
</answer>
</statement>

</task>

<task>
<statement>
<p>
Calculate <m>M_k</m> for each <m>k=1,2,3,4</m> using your results from part (b).
</p>
</statement>
<answer>
<p>
<m>M_1=1, M_2=2, M_3=6, M_4=24</m>
</p>
</answer>
</statement>

</task>

<task>
Expand All @@ -242,12 +244,13 @@
Use Taylor's Theorem to calculate <m>|R_k(1.5)|</m> for each <m>k=1,2,3,4</m>
to 3 decimal places. Use <m>a=1</m> as the center of the approximation.
</p>
</statement>
<answer>
<p>
<m>0.125, 0.042, 0.016, 0.006</m>
</p>
</answer>
</statement>

</task>

<task>
Expand Down Expand Up @@ -313,46 +316,47 @@

<subsection>
<title>Sample Problem</title>
<introduction>
<p>
Here you are tasked with approximating the value of <m>\cos(1)</m>.
</p>
</introduction>
<task>
<statement>
<p>
Calculate the 4th degree Taylor polynomial for <m>f(x)=\cos x</m> centered at <m>\pi</m>,
then use it to approximate the value of <m>\cos(1)</m> to three decimal places.
</p>
</statement>
</task>

<task>
<statement>
<p>
Apply Taylor's Theorem to find an upper bound for the error in this approximation.
</p>
</statement>
</task>
<example>
<introduction>
<p>
Here you are tasked with approximating the value of <m>\cos(1)</m>.
</p>
</introduction>
<task>
<statement>
<p>
Calculate the 4th degree Taylor polynomial for <m>f(x)=\cos x</m> centered at <m>\pi</m>,
then use it to approximate the value of <m>\cos(1)</m> to three decimal places.
</p>
</statement>
</task>

<task>
<statement>
<p>
Use technology to calculate <m>|R_4(1)|</m>. Is the error within the upper bound found
in part (b)?
</p>
</statement>
</task>
<task>
<statement>
<p>
Apply Taylor's Theorem to find an upper bound for the error in this approximation.
</p>
</statement>
</task>

<task>
<statement>
<p>
Explain whether the approximation error <m>|R_{k}(1)|</m> increases or decreases as
<m>k\rightarrow\infty</m>.
</p>
</statement>
</task>
<task>
<statement>
<p>
Use technology to calculate <m>|R_4(1)|</m>. Is the error within the upper bound found
in part (b)?
</p>
</statement>
</task>

<task>
<statement>
<p>
Explain whether the approximation error <m>|R_{k}(1)|</m> increases or decreases as
<m>k\rightarrow\infty</m>.
</p>
</statement>
</task>
</example>

</subsection>

Expand Down
Loading