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 is the instrument of thought, personal expression, and social communication. [BLANK-1]

Which of the following can be said of poetry in early childhood?                         I.          Young children’s enjoyment of poetry will decrease with the inclusion of humor because it too difficult to understand.                         II.         Favorite poems can be memorized and repeated to the teacher or even shared with the entire class.                         III.       Young children enjoy nonsense verse.                            IV.       Poetry for young children stirs emotion, imagination, and creative thinking.        

Discuss some specific ways to enhance and develop oral language in the early childhood grades.

Some of the values of stories for young children are                         I.          they model correct patterns of speech, including vocabulary and comprehension learning.                         II.         giving children enjoyment and relaxation.                         III.       building social skills and values.                         IV.       helping children learn to follow a sequence of events.                         V.        organizing their thoughts and expressing emotions.                         VI.       offering opportunities for children to enjoy the world of pretend or fantasy.

Which statement best reflects the communication expectations for this course?

I have read and understand the course’s Generative AI policy. I understand that generative AI is a professional tool that may be used only as permitted by the course policy. I also understand that using AI in unauthorized ways, including during quizzes or exams, submitting AI-generated work as my own, or using AI to avoid engaging in the learning process, violates the course’s academic integrity expectations.  

Compute the 15th derivative \(f^{(15)}(0)\) of the function \(f(x)=e^{-x^5}\).

Set up the integral that represents the length of the curve \(x=e^{t}-t, \qquad y=4e^{t/2}, \qquad 0\le t\le 2.\)

Final Submission Before picking up your phone, make sure that: You have completed every multiple-choice question. You have completed all free-response questions. You have finished all scratch work. You have written your name on each page at the top right corner. You will not make any further changes to any answer. Picking up your phone begins the final submission process. Once you pick it up, you may not return to the exam questions, revise any answer, or add anything to your handwritten work. 1. Show your work to the webcam Put all pages you wrote on in the correct order, including scratch work. Your free response solutions should be first, with any scratch work afterwards. Before picking up your phone: State aloud: “I have finished the exam and am now beginning the scanning and submission process.” Hold each completed page clearly in front of the webcam, one page at a time. Make sure the entire page is visible. 2. Scan your written work to a PDF You may now use your phone only to scan, transmit, and upload your completed work. iPhone or iPad: Open the built-in Files app, tap the three-dot menu, and select Scan Documents. Android: Open Files by Google and select Scan. You may alternatively use Google Drive or another PDF-scanning app. Scan every page into one PDF. Make sure that: Every page is included. The pages are in the correct order. Every page is readable. No page is sideways or upside down. You may not use your phone to access Canvas, view exam questions, search for information, communicate with another person, access course materials, or use any calculator, AI tool, or other unauthorized resource. 3. Email the PDF to yourself Using your UC email account on your phone, email the PDF to your own UC email address, and CC me at gruberan@ucmail.uc.edu. Use the subject line “Midterm 3 – Last Name, First Name”. The emailed copy provides a timestamped backup, but emailing the PDF does not complete your submission. The PDF uploaded to this Canvas question is your official submission. 4. Retrieve the PDF on your exam computer On the computer running Honorlock, navigate to UC webmail. Open only the message containing the PDF you just sent. Download the attached PDF to your computer. Return to this Canvas question. Do not read, search, or open any other emails or attachments. 5. Upload and submit Upload the PDF to this question, and submit the quiz.

Formula Sheet \(f(x)\) Maclaurin Series Interval of Convergence \(\dfrac{1}{1-x}\) \(\displaystyle\sum_{n=0}^{\infty}x^n\) \((-1,1)\) \(\ln(1-x)\) \(-\displaystyle\sum_{n=1}^{\infty}\frac{x^n}{n}\) \([-1,1)\) \(\ln(1+x)\) \(\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^n}{n}\) \((-1,1]\) \(e^{x}\) \(\displaystyle\sum_{n=0}^{\infty}\frac{x^n}{n!}\) \((-\infty,\infty)\) \(\cos x\) \(\displaystyle\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n)!}\) \((-\infty,\infty)\) \(\sin x\) \(\displaystyle\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n+1}}{(2n+1)!}\) \((-\infty,\infty)\) \(\arctan x\) \(\displaystyle\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n+1}}{2n+1}\) \([-1,1]\) Taylor Remainder Estimate: If \(\left|f^{(N+1)}(c)\right|\le M\) for all numbers \(c\) between \(x\) and \(a\), then the remainder \(R_N(x)\) of the Taylor series satisfies the inequality \(\displaystyle \left|R_N(x)\right|\le\frac{M\left|x-a\right|^{N+1}}{(N+1)!}\) for all numbers between \(x\) and \(a\). Taylor Coefficients: \(\displaystyle c_n=\frac{f^{(n)}(a)}{n!}\)