1131 and 1141 Maple Exam Sample Solutions

1131/1141 Maple Exam Sample Solutions BY: Mary.Mao & Daniel.Chen  Make sure you remember to activate with(LinearAlgebra), with(Student) and with(Plots) Question 1 (Evaluate to a s.f.)

99.9911860107267145728084376707828314

(1)

evalf( 100*sin(93),47); 100*sin(93),47); (2)

Question 2 & Question 3 (Find unique solutions)

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1.580743250

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Question 4 (Expression for Implicit Differentiation)

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0.03239018036

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Question 6 (Integration)

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946.8568397

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Question 7 (Integration)

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0.5412145711

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Question 8 (Integration)

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0.2738092678

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Question 9 (Limit of a Product series)

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[ p:=n^(7/2)*product((2*k/(2*k+7)),k=1..n)] (29)

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Question 10 (Limit of a Sigma series)

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Question 12 (Finding the principal argument of a function, largest)

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2.556918833

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0.9814754536

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0.

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Question 13 (Finding the modulus of a function, largest)

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1.81834680794244

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Question 14 (Function should take a Maple list of complex numbers as its input and return the largest modulus from that list)

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answer imputted: proc (x) options operator, arrow; min(map(abs, x)) end p roc Question 15 (Function should take a Maple list of real numbers as its input and return the smallest cosine from that list)

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answer imputted : proc (x) options operator, arrow; min(map(cos, x)) end proc Question 16 (Finding the number of o f stationary points in a region)

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10

 y

5

0

5  x

10

Therefore 5 stationary points.

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100

 y

50

0

5  x

10

Therefore 5 Stationary Points Question 17, Question 18, Question 19, Question 20, Question 21 (Polar Plots) (with(plots) needed)

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2 4

4

0

1

2

0

3

4

4 2

2 4

4

0

0 1 2 3 4

4

4 2

2 4

4

0

4

1

0

2

4 2

2 4

4

0 10 20 30

4

0

4 2

Question 22 (Finding the implicit Plot and number of solutions)

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10

 y

5

0

5  x

10

Therefore 6 roots

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15

10  y 5

0

5

10

15

 x

Therefore 1 root

Question 23 (Writing the piecewise expression of a function)

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Question 24 (Maple Function for vectors and matrices) (with(LinearAlgebra) needed)

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But alot easier, type it like this and then copy the output and paste it directly into the answer field and it converts it into the relevant format:

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Similarly with the matrix (which is just multiple columns or rows of the 'vec tors'), depending on ease, use either columns or rows (| or , respectively) to seperate them into the matrix

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Question 25 (Analysing LinearAlgebra Package) a) The Maple function "RowOperation" from the LinearAlgebra package can be used to swap two rows of a Matrix M. Which of the following will swap rows 3 and 4 of  M?

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 b) The Maple function "RowOperation" from the LinearAlgebra package can be used to mulitply one row of the Matrix M. Which of the following will multiply row 5 of M  by 2?

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c) The Maple function "RowOperation" from the LinearAlgebra package can be used to add a multiple of one row of the Matrix M to another. Which of the following will replace row 5 of M by row 5 of M plus -4 times row 2 of M?

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Question 26

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Use Maple to create the vector vec tor b that is column 7 from A and the matrix C that is made from columns 1 to 6 and 8 to 9 of A (in the same order as the columns of A).  Now solve the matrix equation: Cx = b Correct Answer: 84491/659407 and enter the 7th component of the unique vector solution for x in the box below. (Your answer should be an exact fraction, not a decimal.) (Column is case-sensitive)

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(SubMatrix is case-sensitive)

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(LinearSolve is Case-sensitive)

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Seventh Component is the 7th solution from the top

Use Maple to create the vector vec tor b that is column 6 from A and the matrix C that is made from columns 1 to 5 and 7 to 10 of A (in the same order as the columns of A).  Now solve the matrix equation dx = b and enter the 8th component of the unique vector solution for x in the box below.

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(Column is case sensitive)

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(SubMatrix is CaseSensitive)

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(LinearSolve is CaseSensitive)

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The 8th component is the value 8th from the top hence

1890994

END OF LAB PRACTICE QUESTIONS Maryizawsm! O____o