1205Test3F06

# 1205Test3F06 - If the Mean Value Theorem can be applied...

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Name Math 1205 Test 3 November 29, 2006 ID # Class Time or CRN READ THE DIRECTIONS. YOU MUST SHOW ALL WORK ON THIS TEST AND USE METHODS LEARNED IN CLASS OR FROM THE WORKSHEETS TO RECEIVE FULL CREDIT. CALCULATORS ARE PERMITTED. Pledge: I have neither given nor received help on this test. Signed 1. Use linearization to estimate 99.9 . 2 . The radius of a circular disk is given as 24 cm with a maximum error in its measurement of 0.2cm. a. Use differentials to estimate the maximum error in the calculated area of the disk. b. Use the part a answer to estimate the percentage error. 3. Find the third degree Taylor Polynomial centered at x = ! 2 for f ( x ) = sin( x ) .

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4. Given f ( t ) = t 3 (4 ! t ) a. Determine all of the critical numbers for f ( t ) . b. Determine the absolute maximum and the absolute minimum f ( t ) on the interval [0, 4]. 5. Can the Mean Value Theorem be applied to the function 2 ( ) x f x e = on the interval [0, 1]? Why or why not?
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Unformatted text preview: If the Mean Value Theorem can be applied, find all values of c that satisfy the theorem. 6. STATE Rolle’s theorem. Then look at the graph below for a function defined on [-1, 1] and mark all numbers c that Rolle’s theorem mentions. 7. Given the graph of f '( x ) below. a. Determine the intervals where f ( x ) is increasing and the intervals where ( ) is decreasing b. List the coordinates of the local maximums of ( ) or state there are none and the coordinates of the local minimums of ( ) or state there are none c. Determine the intervals where the graph of ( ) is concave up and the intervals where the graph of ( ) is concave down d. Find all coordinates of the points of inflection or state there are none e. Sketch a possible graph of y=f(x), if f(0)=0. Bonus: Prove either Rolle’s Theorem using the Mean Value Theorem or Mean Value Theorem using the Rolle’s Theorem....
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1205Test3F06 - If the Mean Value Theorem can be applied...

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The text appears to be a mathematics test with several questions, including problems related to linearization, differentials, Taylor polynomials, critical numbers, the Mean Value Theorem, and graph analysis.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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1205Test3F06

# 1205Test3F06 - If the Mean Value Theorem can be applied...

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Name Math 1205 Test 3 November 29, 2006 ID # Class Time or CRN READ THE DIRECTIONS. YOU MUST SHOW ALL WORK ON THIS TEST AND USE METHODS LEARNED IN CLASS OR FROM THE WORKSHEETS TO RECEIVE FULL CREDIT. CALCULATORS ARE PERMITTED. Pledge: I have neither given nor received help on this test. Signed 1. Use linearization to estimate 99.9 . 2 . The radius of a circular disk is given as 24 cm with a maximum error in its measurement of 0.2cm. a. Use differentials to estimate the maximum error in the calculated area of the disk. b. Use the part a answer to estimate the percentage error. 3. Find the third degree Taylor Polynomial centered at x = ! 2 for f ( x ) = sin( x ) .

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4. Given f ( t ) = t 3 (4 ! t ) a. Determine all of the critical numbers for f ( t ) . b. Determine the absolute maximum and the absolute minimum f ( t ) on the interval [0, 4]. 5. Can the Mean Value Theorem be applied to the function 2 ( ) x f x e = on the interval [0, 1]? Why or why not?
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Unformatted text preview: If the Mean Value Theorem can be applied, find all values of c that satisfy the theorem. 6. STATE Rolle’s theorem. Then look at the graph below for a function defined on [-1, 1] and mark all numbers c that Rolle’s theorem mentions. 7. Given the graph of f '( x ) below. a. Determine the intervals where f ( x ) is increasing and the intervals where ( ) is decreasing b. List the coordinates of the local maximums of ( ) or state there are none and the coordinates of the local minimums of ( ) or state there are none c. Determine the intervals where the graph of ( ) is concave up and the intervals where the graph of ( ) is concave down d. Find all coordinates of the points of inflection or state there are none e. Sketch a possible graph of y=f(x), if f(0)=0. Bonus: Prove either Rolle’s Theorem using the Mean Value Theorem or Mean Value Theorem using the Rolle’s Theorem....
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1205Test3F06 - If the Mean Value Theorem can be applied...

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The text appears to be a mathematics test with several questions, including problems related to linearization, differentials, Taylor polynomials, critical numbers, the Mean Value Theorem, and graph analysis.

TYPE: MULTIPLE_QUESTIONS