Difference between revisions of "022 Exam 2 Sample B"
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<div class="noautonum">__TOC__</div> | <div class="noautonum">__TOC__</div> | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_1|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] == |
<span class="exam">Find the derivative of  <math style="vertical-align: -60%">y\,=\,\ln \frac{(x+1)^4}{(2x - 5)(x + 4)}.</math> | <span class="exam">Find the derivative of  <math style="vertical-align: -60%">y\,=\,\ln \frac{(x+1)^4}{(2x - 5)(x + 4)}.</math> | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_2|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] == |
<span class="exam"> Sketch the graph of <math style="vertical-align: -52%">y = \left(\frac{1}{2}\right)^{x + 1} - 4</math>. | <span class="exam"> Sketch the graph of <math style="vertical-align: -52%">y = \left(\frac{1}{2}\right)^{x + 1} - 4</math>. | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] == |
| − | <span class="exam"> Find the derivative | + | <span class="exam"> Find the derivative of <math style="vertical-align: -18%">f(x) \,=\, 2x^3e^{3x+5}</math>. |
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_4|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] == |
<span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!''' | <span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!''' | ||
| − | <span class="exam">What is the present value of $3000, paid 8 years from now, in an investment that pays 6%interest, | + | <span class="exam">What is the present value of $3000, paid 8 years from now, in an investment that pays 6% interest, |
::<span class="exam">(a) compounded quarterly? | ::<span class="exam">(a) compounded quarterly? | ||
::<span class="exam">(b) compounded continuously? | ::<span class="exam">(b) compounded continuously? | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] == |
| − | <span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1} dx.</math> | + | <span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^{2x} + 1}\, dx.</math> |
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_6|<span class="biglink"><span style="font-size:80%"> Problem 6 </span>]] == |
<span class="exam">Find the area under the curve of  <math style="vertical-align: -13%">y = 6x^2 + 2x</math> between the <math style="vertical-align: -15%">y</math>-axis and <math style="vertical-align: -1%">x = 2</math>. | <span class="exam">Find the area under the curve of  <math style="vertical-align: -13%">y = 6x^2 + 2x</math> between the <math style="vertical-align: -15%">y</math>-axis and <math style="vertical-align: -1%">x = 2</math>. | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_7|<span class="biglink"><span style="font-size:80%"> Problem 7 </span>]] == |
<span class="exam">Find the antiderivatives: | <span class="exam">Find the antiderivatives: | ||
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::<span class="exam">(b) <math>\int_2^54x - 5\,dx.</math> | ::<span class="exam">(b) <math>\int_2^54x - 5\,dx.</math> | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_8|<span class="biglink"><span style="font-size:80%"> Problem 8 </span>]] == |
<span class="exam"> | <span class="exam"> | ||
Find the quantity that produces maximum profit, given demand function <math style="vertical-align: -15%">p = 70 - 3x</math> and cost function  <math style="vertical-align: -8%">C = 120 - 30x + 2x^2.</math> | Find the quantity that produces maximum profit, given demand function <math style="vertical-align: -15%">p = 70 - 3x</math> and cost function  <math style="vertical-align: -8%">C = 120 - 30x + 2x^2.</math> | ||
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_9|<span class="biglink"><span style="font-size:80%"> Problem 9 </span>]] == |
<span class="exam"> | <span class="exam"> | ||
| − | Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the | + | Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the local minimum and which is the local maximum (i.e., which test did you use?). |
| − | == [[ | + | == [[022_Exam_2_Sample_B,_Problem_10|<span class="biglink"><span style="font-size:80%"> Problem 10 </span>]] == |
<span class="exam">'''Use calculus to set up and solve the word problem:''' | <span class="exam">'''Use calculus to set up and solve the word problem:''' | ||
A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost). | A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost). | ||
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| + | '''Contributions to this page were made by [[Contributors|John Simanyi]]''' | ||
Latest revision as of 16:13, 14 November 2016
This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the boxed problem numbers to go to a solution.
Problem 1
Find the derivative of
Problem 2
Sketch the graph of .
Problem 3
Find the derivative of .
Problem 4
Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!
What is the present value of $3000, paid 8 years from now, in an investment that pays 6% interest,
- (a) compounded quarterly?
- (b) compounded continuously?
Problem 5
Find the antiderivative of
Problem 6
Find the area under the curve of between the -axis and .
Problem 7
Find the antiderivatives:
- (a)
- (b)
Problem 8
Find the quantity that produces maximum profit, given demand function and cost function
Problem 9
Find all relative extrema and points of inflection for the function . Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the local minimum and which is the local maximum (i.e., which test did you use?).
Problem 10
Use calculus to set up and solve the word problem: A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4th side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).
Contributions to this page were made by John Simanyi