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MATH 142 Final: MATH142 South Carolina 17Final Exam2

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turquoisegnu128

15 Feb 2019

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Instructions: this exam comes in two parts. (1) hand in part. Hand in only this part. (2) statement of multiple choice problems. You can take this part home to learn from and to check your answers once the solutions are posted: on problem 0, ll in the blanks. Check that your copy of the exam has all of the problems: upon request, you will be given as much (blank) scratch paper as you need, during the exam, the use of unauthorized materials is prohibited. Unauthorized materials include: books, electronic devices, any device with which you can connect to the internet, and personal notes. This means no electronic devices (such as cell phones) allowed in your pockets. At a student"s request, i will project my watch upon the projector screen: during this exam, do not leave your seat unless you have permission. If you have a question, raise your hand.

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Using the function y = f(x) obtained in (c), find the .y coordinate corresponding to the value x = -1 / 2 Evaluate both formulas for dy / dx at this point. Why do you think this happens.? Using the explicit derivative formula dy / dx = f (x) obtained in part (c) , find all points on the graph of y = f(x) where the tangent line is horizontal. Then substitute the x and y - coordinates of each such point into the implicit dy / dx formula given in part(b). Again, why does this happen? Again using the explicit derivative formula dy / dx = f(x) from part (c). find all points on the graph of f where the tangent slope equals 6. Now substitute the x- and y- coordinates of each such point into the implicit dy / dx formula given in part (b) to confirm this slope value. It is clear that no point (x, y) for which x + 2y = 0 will appear on the graph of original equation 2x = y - x2 / x +2y. In effect, points on the line x + 2y = 0 are "cut out" of the graph of the function f Relate this observation to the phenomena encountered earlier in parts (e) and (f). Once again referring to the explicit function f(x) obtained in part (c), where does the graph of f have a vertical asymptote? What happens when you substitute this X-value into the original implicit equation (given at the beginning of this worksheet) and attempt to solve for y ? Explain. [ Verification of the implicit derivative given in part (b).] Implicitly differentiate the equation 2x = y - x2 / x = 2y, applying the quotient role on the right-hand side. Clear the denominator and expand terms, then solve for dy / dx and simplify. Note: Solutions to this problem set are t0 be established by traditional algebraic or arithmetic means. using Maple software to verify each result To download the Maple template file prepared to assist you w ith these exercises, go to https;//my,ltu edu and login, select Calculus 1 and click on Workshop. Saw this file to your laptop hard drive and exit the web Hand-generated solutions are to be fully documented In the workshop report including all steps requiring algebraic or calculus computations - merely listing the answers produce with Maple is not sufficient. Printouts of your Maple verifications are required as part of your workshop report. Consider the equation 2x = y -x2 / x+ 2y. Verify that the points .A(1, -1) and B(-2, 4/3) lie on the graph of this equation. In part (j) of this worksheet you will be asked to verify- the derivative formula by implicitly differentiating the equation given above. Evaluate this derivative at points A and B. Solve for y in the original equation, expressing y as an explicit function of x. (For later reference, we will call this function f(x).) Compute dy / dx from this expression and simplify , then evaluate this explicit version of dy / dx at both A aud B. Considering the results of part (b), are these the values you expected? Why or why not? Evaluate each of the two formulas for dy / dx (both implicit and explicit) at the point C(-1, 0). Can you explain your results?

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Using the function y = f(x) obtained in (c), find the .y coordinate corresponding to the value x = -1 / 2 Evaluate both formulas for dy / dx at this point. Why do you think this happens.? Using the explicit derivative formula dy / dx = f (x) obtained in part (c) , find all points on the graph of y = f(x) where the tangent line is horizontal. Then substitute the x and y - coordinates of each such point into the implicit dy / dx formula given in part(b). Again, why does this happen? Again using the explicit derivative formula dy / dx = f(x) from part (c). find all points on the graph of f where the tangent slope equals 6. Now substitute the x- and y- coordinates of each such point into the implicit dy / dx formula given in part (b) to confirm this slope value. It is clear that no point (x, y) for which x + 2y = 0 will appear on the graph of original equation 2x = y - x2 / x +2y. In effect, points on the line x + 2y = 0 are "cut out" of the graph of the function f Relate this observation to the phenomena encountered earlier in parts (e) and (f). Once again referring to the explicit function f(x) obtained in part (c), where does the graph of f have a vertical asymptote? What happens when you substitute this X-value into the original implicit equation (given at the beginning of this worksheet) and attempt to solve for y ? Explain. [ Verification of the implicit derivative given in part (b).] Implicitly differentiate the equation 2x = y - x2 / x = 2y, applying the quotient role on the right-hand side. Clear the denominator and expand terms, then solve for dy / dx and simplify. Note: Solutions to this problem set are t0 be established by traditional algebraic or arithmetic means. using Maple software to verify each result To download the Maple template file prepared to assist you w ith these exercises, go to https;//my,ltu edu and login, select Calculus 1 and click on Workshop. Saw this file to your laptop hard drive and exit the web Hand-generated solutions are to be fully documented In the workshop report including all steps requiring algebraic or calculus computations - merely listing the answers produce with Maple is not sufficient. Printouts of your Maple verifications are required as part of your workshop report. Consider the equation 2x = y -x2 / x+ 2y. Verify that the points .A(1, -1) and B(-2, 4/3) lie on the graph of this equation. In part (j) of this worksheet you will be asked to verify- the derivative formula by implicitly differentiating the equation given above. Evaluate this derivative at points A and B. Solve for y in the original equation, expressing y as an explicit function of x. (For later reference, we will call this function f(x).) Compute dy / dx from this expression and simplify , then evaluate this explicit version of dy / dx at both A aud B. Considering the results of part (b), are these the values you expected? Why or why not? Evaluate each of the two formulas for dy / dx (both implicit and explicit) at the point C(-1, 0). Can you explain your results?

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Show transcribed image text A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x Ã C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/16/ Homework Sets HW4 EigenValues Rod: Problem 16 Prev Up Next HW4 EigenValues Rod Problem 16 Password/Email Result Entered 01,74 48 56 Answer Preview Grades Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 The answer above is NOT correct (1 pt) 8 0.25 Let: A 27 -2 Find an invertible S and a diagonal D such that S AS-D 0 6 Preview Answers Submit Answers Your score was recorded You have attempted this problem 2 times. You received a score of 0% for this attempt. Your overall recorded score is 0% You have unlimited attempts remaining Activate Windows Go to Settings to activate Windows 10:58 PMM 12/1/20 ^
S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/17/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 17 Prev Up Next (1 pt) Find a 2 Ã 2 matrix A for which HW4 EigenValues Rod Problem 17 Password/Email Grades .5 E-spanand E span Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 where Ex is the eigenspace associated with the eigenvalueA .4 Note: You can eam partial credit on this probvem. Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:58 PMM 12/1/20 ^
S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C O Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/18/ Homework Sets HW4 EigenValues Rod: Problem 18 Prev Up Next HW4 EigenValues Rod Problem 18 Password/Email Entered Answer Preview Result incorrect Grades Problems ncorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 incorrect At least one of the answers above is NOT correct (1 pt) Find a 2 x 2 matrix A such that and -5 -3 are eigenvectors of A, with eigenvalues 5 and-10 respectively. Activate Windows Go to Settings to activate Windows Note: You can eam partial credit on this probvem. 10:58 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x Ã Ð¡ Not secure I webworks2.csuohio.edu/webwork2/CSU-MTH284-Fall 18/HW4-EigenValue r-2699769&effectivelser=2699769&key=vYsrs1KsSmrZ4iwgsvaFAE 1PYWli â Logged in as 2699769 Log Out MATHEMATICAL ASSOCIATION OF AMERICA MAIN MENU Courses Homework Sets webwork/csu mth284 fall18I hw4_e eigenvaluesrod 20 HW4 EigenValues Rod: Problem 20 Prev Up Next (1 pt) HW4 EigenValues Rod Problem 20 Password/Email Grades 13 10 Problems Let M 5 -2 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Find formulas for the entries of M, where n is a positive integer An-(n-1) Mn = Note: You can eam partial credit on this problem. Preview Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0% You have unlimited attempts remaining. Activate Windows Go to Settings to activate Windows Email instructor CSU MTH284 Fall13/HW4 EigenValues Rod21. 10:58 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/21/ Homework Sets HW4 EigenValues Rod: Problem 21 Prev Up Next HW4 EigenValues Rod Problem 21 Password/Email Entered AC Answer Preview Grades AC Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 The answer above is NOT correct (1 pt) Which of the following transformations are linear? A. D.10 Ð£Ð· 2x1 Activate Windows Go to Settings to activate Windows Preview Answers Submit Answers Your score was recorded. You have attempted this problem 2 times 10:59 PMM 12/1/20 ^
S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/23/ Homework Sets HW4 EigenValues Rod: Problem 23 Prev Up Next HW4 EigenValues Rod Problem 23 Password/Email Entered Answer Preview Result Grades incorret Problems incorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 At least one of the answers above is NOT correct 3-6 21is a basis for IR (1 pt) The set B Find the coordinates of the vector relative to the basis B Note: You can eam partial credit on this probvem. Preview Answers Submit Answers Your score was recorded You have attempted this problem 3 times. You received a score of 0% for this attempt. Your overall recorded score is 0%. You have unlimited attempts remaining Activate Windows Go to Settings to activate Windows Email instructor 10:59 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/24/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 24 Prev Up Next HW4 EigenValues Rod Problem 24 Password/Email Grades (1 pt) The vectors -2 -3 Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 form a basis for R3 if and only if k38/11 Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:59 PMM 12/1/20 ^