(11)(11)

(3)(3)

(7)(7)

(6)(6)

(2)(2)

(5)(5)

(10)(10)

(1)(1)

(8)(8)

(9)(9)

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

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

Question 2 & Question 3 (Find unique solutions)

1.580743250

Question 4 (Expression for Implicit Differentiation)

(19)(19)

(21)(21)

(15)(15)

(12)(12)

(22)(22)

(17)(17)

(20)(20)

(13)(13)

(18)(18)

(16)(16)

(14)(14)

0.03239018036

Question 6 (Integration)

946.8568397

Question 7 (Integration)

(28)(28)

(30)(30)

(24)(24)

(23)(23)

(31)(31)

(29)(29)

(26)(26)

(27)(27)

(25)(25)

0.5412145711

Question 8 (Integration)

0.2738092678

Question 9 (Limit of a Product series)

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

Question 10 (Limit of a Sigma series)

(44)(44)

(32)(32)

(34)(34)

(40)(40)

(37)(37)

(42)(42)

(38)(38)

(33)(33)

(39)(39)

(36)(36)

(41)(41)

(35)(35)

(43)(43)

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

2.556918833

0.9814754536

0.

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

(45)(45)

(47)(47)

(32)(32)

(46)(46)

(48)(48)

1.81834680794244

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

answer imputted: proc (x) options operator, arrow; min(map(abs, x)) end proc

Question 15 (Function should take a Maple list of real numbers as its input andreturn the smallest cosine from that list)

answer imputted : proc (x) options operator, arrow; min(map(cos, x)) end proc

Question 16 (Finding the number of stationary points in a region)

x0 5 10

y 5

10

Therefore 5 stationary points.

(32)(32)

(50)(50)

(51)(51)

(49)(49)

(52)(52)

x0 5 10

y 50

100

Therefore 5 Stationary Points

Question 17, Question 18, Question 19, Question 20, Question 21 (Polar Plots) (with(plots) needed)

(55)(55)

(32)(32)

(53)(53)

(54)(54)

0 1 2 30

4

2

4

4

2

4

0 1 2 3 40

4

2

4

4

2

4

(32)(32)

(53)(53)

(56)(56)

(57)(57)

0 1 20

4

2

4

4

2

4

0 10 20 300

4

2

4

4

2

4

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

(32)(32)

(53)(53)

(58)(58)

(59)(59)

x0 5 10

y 5

10

Therefore 6 roots

(60)(60)

(32)(32)

(53)(53)

(61)(61)

x0 5 10 15

y

5

10

15

Therefore 1 root

Question 23 (Writing the piecewise expression of a function)

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

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

(32)(32)

(53)(53)

(63)(63)

(65)(65)

(67)(67)

(64)(64)

(62)(62)

(66)(66)

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

Question 25 (Analysing LinearAlgebra Package)

a) The Maple function "RowOperation" from the LinearAlgebra package can be usedto swap two rows of a Matrix M. Which of the following will swap rows 3 and 4 ofM?

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

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

(32)(32)

(53)(53)

(69)(69)

(68)(68)

Question 26

(32)(32)

(53)(53)

(71)(71)

(70)(70)

Use Maple to create the vector b that is column 7 from A and the matrix C that is madefrom 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:84491/659407and 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)

(SubMatrix is case-sensitive)

(LinearSolve is Case-sensitive)

(72)(72)

(32)(32)

(53)(53)

(73)(73)

Seventh Component is the 7th solution from the top

Use Maple to create the vector 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.

(Column is case sensitive)

(75)(75)

(72)(72)

(32)(32)

(53)(53)

(74)(74)

(SubMatrix is CaseSensitive)

(LinearSolve is CaseSensitive)

(76)(76)

(72)(72)

(32)(32)

(53)(53)

(74)(74)

The 8th component is the value 8th from the top hence 1890994

END OF LAB PRACTICE QUESTIONS Maryizawsm! O____o