Difference between revisions of "022 Exam 2 Sample A"
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<span class="exam">Find the derivative of  <math style="vertical-align: -40%">y\,=\,\ln \frac{(x+5)(x-1)}{x}.</math> | <span class="exam">Find the derivative of  <math style="vertical-align: -40%">y\,=\,\ln \frac{(x+5)(x-1)}{x}.</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"> Problem 2 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] == |
<span class="exam"> Find the antiderivative of  <math style="vertical-align: -10%">y\,=\,3x^2-12x+8.</math> | <span class="exam"> Find the antiderivative of  <math style="vertical-align: -10%">y\,=\,3x^2-12x+8.</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_3|<span class="biglink"> Problem 3 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] == |
<span class="exam"> Find the antiderivative of <math style="vertical-align: -50%">\int \frac{1}{3x+2}\,dx.</math> | <span class="exam"> Find the antiderivative of <math style="vertical-align: -50%">\int \frac{1}{3x+2}\,dx.</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_4|<span class="biglink"> Problem 4 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_4|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] == |
<span class="exam"> Find the antiderivative of <math style="vertical-align: -45%">\int (3x+2)^4\,dx.</math> | <span class="exam"> Find the antiderivative of <math style="vertical-align: -45%">\int (3x+2)^4\,dx.</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_5|<span class="biglink"> Problem 5 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] == |
<span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers - not solve for particular values!''' | <span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers - not solve for particular values!''' | ||
| Line 17: | Line 17: | ||
::<span class="exam">(a) compounded monthly? | ::<span class="exam">(a) compounded monthly? | ||
::<span class="exam">(b) compounded continuously? | ::<span class="exam">(b) compounded continuously? | ||
| − | == [[022_Exam_2_Sample_A,_Problem_6|<span class="biglink"> Problem 6 </span>]] == | + | == [[022_Exam_2_Sample_A,_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: -60%">y\,=\,\frac{8}{\sqrt{x}}</math>  between <math style="vertical-align: -5%">x=1</math> and <math style="vertical-align: -5%">x=4</math>. | <span class="exam">Find the area under the curve of  <math style="vertical-align: -60%">y\,=\,\frac{8}{\sqrt{x}}</math>  between <math style="vertical-align: -5%">x=1</math> and <math style="vertical-align: -5%">x=4</math>. | ||
| − | == [[022_Exam_2_Sample_A,_Problem_7|<span class="biglink"> Problem 7 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_7|<span class="biglink"><span style="font-size:80%"> Problem 7 </span>]] == |
<span class="exam">Find the quantity that produces maximum profit, given the demand function <math>p\,=\,90-3x</math> and cost function <math>C\,=\,200-30x+x^2</math>. | <span class="exam">Find the quantity that produces maximum profit, given the demand function <math>p\,=\,90-3x</math> and cost function <math>C\,=\,200-30x+x^2</math>. | ||
| − | == [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"> Problem 8 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"><span style="font-size:80%"> Problem 8 </span>]] == |
<span class="exam"> | <span class="exam"> | ||
Use diferentials to approximate the change in profit given <math>x = 10</math> uunits and <math>dx = 0.2</math> units. <math>P = -4x^2 + 90x - 128</math> | Use diferentials to approximate the change in profit given <math>x = 10</math> uunits and <math>dx = 0.2</math> units. <math>P = -4x^2 + 90x - 128</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_9|<span class="biglink"> Problem 9 </span>]] == | + | == [[022_Exam_2_Sample_A,_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 following function. Be sure to give coordinate pairs for each point. You do not need to draw the graph. <math>g(x) = \frac{2}{3}x^3 + x^2 - 12x</math> | Find all relative extrema and points of inflection for the following function. Be sure to give coordinate pairs for each point. You do not need to draw the graph. <math>g(x) = \frac{2}{3}x^3 + x^2 - 12x</math> | ||
| − | == [[022_Exam_2_Sample_A,_Problem_10|<span class="biglink"> Problem 10 </span>]] == | + | == [[022_Exam_2_Sample_A,_Problem_10|<span class="biglink"><span style="font-size:80%"> Problem 10 </span>]] == |
<span class="exam"> | <span class="exam"> | ||
Use calculus to set up and solve the word problem: Find the length and width of a rectangle that has perimeter 48 meters and maximum area. | Use calculus to set up and solve the word problem: Find the length and width of a rectangle that has perimeter 48 meters and maximum area. | ||
Revision as of 13:37, 13 May 2015
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\,=\,\ln \frac{(x+5)(x-1)}{x}.}
Problem 2
Find the antiderivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\,=\,3x^2-12x+8.}
Problem 3
Find the antiderivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{3x+2}\,dx.}
Problem 4
Find the antiderivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int (3x+2)^4\,dx.}
Problem 5
Set up the equation to solve. You only need to plug in the numbers - not solve for particular values!
How much money would I have after 6 years if I invested $3000 in a bank account that paid 4.5% interest,
- (a) compounded monthly?
- (b) compounded continuously?
Problem 6
Find the area under the curve of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\,=\,\frac{8}{\sqrt{x}}} between Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=1} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=4} .
Problem 7
Find the quantity that produces maximum profit, given the demand function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p\,=\,90-3x} and cost function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C\,=\,200-30x+x^2} .
Problem 8
Use diferentials to approximate the change in profit given Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = 10} uunits and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dx = 0.2} units. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P = -4x^2 + 90x - 128}
Problem 9
Find all relative extrema and points of inflection for the following function. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g(x) = \frac{2}{3}x^3 + x^2 - 12x}
Problem 10
Use calculus to set up and solve the word problem: Find the length and width of a rectangle that has perimeter 48 meters and maximum area.