Preparation Problems#
Complete all preparation problems before class time on the scheduled date.
Week 15#
Day 15A: Monday, December 4th
Find the area of the region:
bounded below by \(y=-e^{2x}\)
bounded above by \(y=3x^2+1\)
bounded on the sides by \(x=0\) and \(x=2\).
Day 15B: Wednesday, December 6th
No prep problem for today.
Day 15C: Friday, December 8th
No prep problem for today.
Week 14#
Day 14A: Monday, November 27th
Use integration by parts to calculate the integral:
Day 14B: Wednesday, November 29th
Compute the area under the given curve:
Day 14C: Friday, December 1st
No prep problem for today.
Week 13#
Day 13A: Monday, November 20th
Evaluate the following definite integral. Use integral and evaluation notation in your work.
Day 13B: Wednesday, November 22nd
Thanksgiving Recess. No preparation for today.
Day 13C: Friday, November 24th
Thanksgiving Recess. No preparation for today.
Week 12#
Day 12A: Monday, November 13th
Write down 5 different antiderivatives of the function \(f(x)=\dfrac{1}{3}x^3\).
Day 12B: Wednesday, November 15th
Use the substitution rule to calculate the following integral:
Day 12C: Friday, November 17th
Use the substitution rule to calculate the following integral:
Week 11#
Day 11A: Monday, November 6th
No prep problem for today.
Day 11B: Wednesday, November 8th
Given the equation \(3x^2+6y^2=33\). Calculate \(\dfrac{dy}{dt}\) at a time when \(x=3\), \(y=1\) and \(\dfrac{dx}{dt}=4\).
Day 11C: Friday, November 10th
Use the given Elasticity of Demand to determine an approximation for the percentage change in revenue caused by a \(1\%\) increase in price for each of the following values of \(E\):
\(E=\dfrac{1}{5}\)
\(E= 5\)
\(E=1\)
Week 10#
Day 10A: Monday, October 30th
No prep problem for today.
Day 10B: Wednesday, November 1st
Calculate the second derivative of the following functions:
\(f(x)=4x^3+5x-6\)
\(g(x)=\\drac{4}{x^2}+6\\ln(x)\)
Day 10C: Friday, November 3rd
Find and classify all critical points of the following function. Use the second derivative to classify the critical points.
Week 9#
Day 9A: Monday, October 23rd
Find the possible extreme locations for the function:
Day 9B: Wednesday, October 25th
Use the first derivative to find and classify the critical numbers for the function:
Day 9C: Friday, October 27th
No prep problem for today.
Week 8#
Day 8A: Monday, October 16th
Given functions \(f(x)=3x^2+4x\) and \(u(x)=\sqrt{x}\) calculate the following compositions:
\(f(u(x))\)
\(u(f(x))\)
Day 8B: Wednesday, October 18th
Differentiate the following functions. Show the chain rule step in your work.
\(f(x)=\ln \left( x^3+5 \right)\)
\(g(x)=\ln \left( (4x+6)^5 \right)\)
Day 8C: Friday, October 20th
Calculate \(\dfrac{dy}{dx}\) given the following equation:
Week 7#
Day 7A: Monday, October 9th
No preparation problem assigned for today.
Day 7B: Wednesday, October 11th
Use the product rule to differentiate the following functions. Show all work.
\(f(x)=x^4(3x^2+5x)\)
\(g(x)=\sqrt{x}(4x-6)\)
Day 7C: Friday, October 13th
Use the quotient rule to differentiate the following functions. Show all work.
\(f(x)=\dfrac{3x+1}{x^2+7}\)
\(g(x)=\dfrac{6x^3-x}{5x-2}\)
Week 6#
Day 6A: Monday, October 2nd
No preparation problem assigned for today.
Day 6B: Wednesday, October 4th
Use the power rule to differentiate:
\(f(x)=x^4\)
\(g(x)=x^{10}\)
\(f(x)=\sqrt[3]{x}\)
Day 6C: Friday, October 6th
Differentiate the following functions:
\(f(x)=6x^4\)
\(g(x)=\dfrac{x^{10}}{3}\)
\(f(x)=\dfrac{\sqrt[3]{x}}{4}\)
\(h(x)=\dfrac{7}{x^4}\)
Week 5#
Day 5A: Monday, September 25th
No preparation problem assigned for today.
Day 5B: Wednesday, September 27th
Organize and bring all of your completed notes, problems, and papers with you to class.
Day 5C: Friday, September 29th
Study for Midterm Exam 1
Week 4#
Day 4A: Monday, September 18th
L1: Draw the graph of a function \(f(x)\) that satisfies all of the following properties:
\(\displaystyle \lim_{x\to 0^-} f(x)=-2\)
\(\displaystyle \lim_{x\to 0^+} f(x)=3\)
\(f(0)=1\)
\(\displaystyle \lim_{x\to 3^-} f(x)=-\infty\)
\(\displaystyle \lim_{x\to 3^+} f(x)=+\infty\)
Day 4B: Wednesday, September 20th
L3: Evaluate the following limits algebraically. (Factor the numerator and denominator as much as possible, and remember to use the limit notation in your work.)
\(\displaystyle \lim_{x\to 0} \dfrac{3x^2-2x}{5x}\)
\(\displaystyle \lim_{x\to -2} \dfrac{x^2+4x+4}{x+2}\)
Day 4C: Friday, September 22nd
Using the table of S&P 500 values from our notes, calculate the average rate of change over the 3-year period 2009-2012.
Week 3#
Day 3A: Monday, September 11th
F5: Simplify each exponential expression into a single term of the form \(3^{kx}\). Show all steps.
\(\sqrt{3^{4x}\cdot 3^{-2x}}\)
\( \left(\dfrac{3^{2x}}{3^{5x}}\right)^3\)
Day 3B: Wednesday, September 13th
F7: Write each expression into a single logarithm. Show all steps.
\(\ln(5)+3\ln(2)\)
\(3\ln(x)+2\ln(2x-5)-4\ln(x^2+1)\)
Day 3C: Friday, September 15th
L1: Write out a table with 8 input and function value pairs showing a function \(f(x)\) satisfying the following limit:
(Use the table given in the first example as a guide for what your response should look like.)
Week 2#
Day 2A: Monday, September 4th
No preparation problems assigned for today.
Day 2B: Wednesday, September 6th
F3: On Wednesday, a small bicycyle shop notices that it costs \(\$10,000\) to produce 20 electric bicycles. The following week, they notice that it costs \(\$15,000\) to produce 25 electric bicycles. Find a linear cost function.
Day 2C: Friday, September 8th
F4: Consider the quadratic function: \(f(x)=x^2-10x+9\), find the coordinates for the:
Vertex
\(y\)-intercept(s)
\(x\)-intercept(s)
Week 1#
Day 1A: Monday, August 28th
No preparation problems assigned for today.
Day 1B: Wednesday, August 30th
F1: Given the function: \(f(x)=\dfrac{x^3}{4}-5\sqrt{x}\), evaluate the following expressions. First write the unsimplified value, and then the simplified value.
\(f(4)\)
\(f(36)\)
Day 1C: Friday, September 1st
F3: Find an equation for the line through the points \((3,4)\) and \((-4,2)\).