007A Sample Midterm 2 - Revision history

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2017-11-12T00:42:56Z

Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 7A for the midterm. An actual test may or may not be similar.''' '''Click on the''' '''<s..."

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'''This is a sample, and is meant to represent the material usually covered in Math 7A for the midterm. An actual test may or may not be similar.'''

'''Click on the''' '''<span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''
<div class="noautonum">TOC</div>

== [[007A_Sample Midterm 2,_Problem_1|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==
<span class="exam"> Evaluate the following limits.

<span class="exam">(a) Find  <math style="vertical-align: -14px">\lim _{x\rightarrow 2} \frac{\sqrt{x^2+12}-4}{x-2}</math>

<span class="exam">(b) Find  <math style="vertical-align: -19px">\lim _{x\rightarrow 0} \frac{\sin(3x)}{\sin(7x)} </math>

<span class="exam">(c) Evaluate  <math style="vertical-align: -16px">\lim _{x\rightarrow 0} x^2\cos\bigg(\frac{1}{x}\bigg) </math>

== [[007A_Sample Midterm 2,_Problem_2|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==
<span class="exam"> Use the definition of the derivative to find   <math>\frac{dy}{dx}</math>   for the function  <math style="vertical-align: -12px">y=\frac{1+x}{3x}.</math>

== [[007A_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] ==
<span class="exam"> Find the derivatives of the following functions. '''Do not simplify.'''

<span class="exam">(a)   <math style="vertical-align: -5px">f(x)=x^3(x^{\frac{4}{3}}-1)</math>

<span class="exam">(b)   <math style="vertical-align: -14px">f(x)=\frac{x^3+x^{-3}}{1+6x}</math>  where  <math style="vertical-align: 0px">x>0</math>

<span class="exam">(c)   <math style="vertical-align: -5px">f(x)=\sqrt{3x^2+5x-7}</math>  where  <math style="vertical-align: 0px">x>0</math>

== [[007A_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==
<span class="exam"> Assume  <math style="vertical-align: -5px">N(t)</math>  denotes the size of a population at time  <math style="vertical-align: 0px">t</math>  and that  <math style="vertical-align: -5px">N(t)</math>  satisfies the equation:

::<math>\frac{dN}{dt}=3N\bigg(1-\frac{N}{20}\bigg).</math>

<span class="exam"> Let  <math style="vertical-align: -16px">f(N)=3N\bigg(1-\frac{N}{20}\bigg),~N\ge 0.</math>  Graph  <math style="vertical-align: -5px">f(N)</math>  as a function of  <math style="vertical-align: 0px">N</math>  and identify all equilibria. That is, all points where  <math style="vertical-align: -15px">\frac{dN}{dt}=0.</math>

== [[007A_Sample Midterm 2,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
<span class="exam"> A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the string has been let out?

'''Contributions to this page were made by [[Contributors|Kayla Murray]]'''