Practice Quiz 10
.pdf
School
University of London**We aren't endorsed by this school
Course
MARKETING 123
Subject
Mathematics
Date
Dec 17, 2024
Pages
5
Uploaded by CommodoreGiraffe3325
MATH 137 Quiz 10Wednesday, November 29, 2023. Duration: 35 minutes.Notes:1. Answer all questions in the space provided.2. For multiple choice and true/false questions, answer by filling in the bubble on the lastpage of the quiz.3. Your grade will be influenced by how clearly you express your ideas and how well youorganize your solutions. Show all details to get full marks. Numerical answers should bein exact values (no approximations).4. No calculators are allowed.5. There are a total of 20 possible points.6. DO NOT write on the Crowdmark QR code at the top of the pages or your quiz will notbe scanned (and will receive a grade of zero).7. Use a dark pen or pencil.
(MC) Answer the following multiple choice questions on the last page of the quiz. Bubble (a),(b), (c), or (d). Note there is only one correct answer for each question.[6]1. Which isNOTan indeterminate form?(a) 00(b) 0∞(c) 1∞(d) None of the above2. Suppose thatf′(x) = 3x(x−1)(x+ 1)2. How manylocal maximadoesf(x) have?(a) 0.(b) 1.(c) 2.(d) 3.3. limx→12x3−x2−4x+ 34x3−8x2+ 4x(a) Does not exist(b)23(c)54(d) None of the above(TF) Answer the following true or false questions on the last page of the quiz. Bubble (a) forTrue, (b) for False.[2]4. TRUE or FALSE: Suppose that (c, f(c)) is a critical point. Iff′′(c) = 0, then (c, f(c))is neither a local max nor min.5. TRUE or FALSE: For differentiable functionsfandg, if limx→af(x)g(x)=L, then limx→af′(x)g′(x)=L
(SA) Short answer questions, marks only awarded for a correct final answer, you do not need toshow any work.1.Evaluate the limit limx→1xa−1xb−1wherea, b∈Randb̸= 0.[2]2.Evaluate the limit limx→∞x+ sinxx[2](LA) The remaining questions are long answer questions, please show all of your work.1.Find and classify the local extrema off(x) =x+ 2x−2+x.[4]
2.Letf(x) =ax3+bx2+cx+dbe a cubic polynomial.[4]Determinea, b, c, d∈Rsuch thatf(x) has a local minimum at (0,1) and a localmaximum at (2,9). State the resulting polynomial.
This page is meant for rough work. Clearly indicate in the original question if part of your solution is here.