Maple Online Tutorial Test-all-v1 PDF

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Maple Lab Test Practice Questions w/ Answers
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University of New South Wales -

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Find a decimal approximation to  correct to

significant figures and enter your

answer in the box below.

Find, to 10 significant figures, the unique turning point of

in the interval [1,2] and enter it in the box below. =



Find, to 10 significant figures, the value of the second derivative of

at the turning point, that is

.

Enter your answer in the box below. =



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Find, to 10 significant figures, the unique turning point of

in the interval [0,0.4] and enter it in the box below. =



Find, to 10 significant figures, the value of the second derivative of

at the turning point, that is

.

Enter your answer in the box below. =





Suppose

determines

as a function of

. Assuming that

the Maple command  eqn := x^4 + x^2*(y-1)^2 + y^4 = 4; has been executed, which of the following Maple expressions would find

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a) The Maple expression for the

is

 b) The Maple expression for the constant

is

 c) The Maple expression for

is

 d) Evaluate, to 10 significant figures,

and enter your answer in the box below.





a) The Maple expression for the inverse tan of x is

 b) The Maple expression for the constant

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is

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 c) The Maple expression for the imaginary unit (square root of -1) is

 d) Evaluate, to 10 significant figures,

and enter your answer in the box below.





a) The Maple expression for cosec(x) is

 b) The Maple expression for the constant

is

 c) The Maple expression for

is



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d) Evaluate, to 10 significant figures,

and enter your answer in the box below.





a) The Maple expression for the inverse cot of x is

 b) The Maple expression for the constant

is

 c) The Maple expression for

is

 d) Evaluate, to 10 significant figures,

and enter your answer in the box below.





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Find  and enter your answer in the box below. You must enter the exact result in Maple syntax.

Find  and enter your answer in the box below. You must enter the exact result in Maple syntax.

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Find approximations to all 5 roots of the polynomial

and enter them in the box below. Your approximations should be correct to 10 significant figures. You must enter the roots as a Maple list, that is, enclosed in square brackets. For example, a typical answer would be similar to:



[-.8724241534, -.1573479856-.7588819850*I, -.1573479856+.7588819850*I, .7991119175, 2.388008207]

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Find the principal arguments of the 5 roots of the polynomial

and enter a decimal approximation to the largest principal argument in the box below. Your approximation should be correct to 10 significant



figures.

Find the moduli of the 5 roots of the polynomial

and enter a decimal approximation to the largest modulus in the box below. Your approximation should be correct to 10 significant figures.

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

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To answer this question you need to create a Maple function using Maple's arrow (->) notation. Your function should take a Maple list of complex



numbers as its input and return the largest modulus from that list. Enter your function in the box below.

To answer this question you need to create a Maple function using Maple's arrow (->) notation. Your function should take a Maple list of real



numbers as its input and return the smallest cosine from that list. Enter your function in the box below.

Plot the graph y = f(x) for f(x) = How many many stationary points does f have in the interval [-10,10]? Enter your answe below. To avoid typing errors you can copy and paste the following Maple command. f := (3072*x^7+19712*x^6-2688*x^5-213360*x^4-225988*x^3+752199*x^2+1584660*x)/(215

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Select the option below which is the plot of the polar curve . for

.





Select the option below which is the plot of the polar curve . for

.



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

Select the option below which is the plot of the polar curve . for

.





Select the option below which is the plot of the polar curve . for

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



Select the option below which is the plot of the polar curve . for

.





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Plot the two curves defined by

and  and find the number of intersections of these curves in the square

Enter the number of intersections in the box below.



Let

and

.

(a)



(b) The area of the parallelogram spanned by is

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

Note: In the package LinearAlgebra, the Maple comand of the dot product of u and v is u.v  The Maple comand of the cross product u v is u &x v



The Mean Value Theorem . Suppose that such that

Find the real number

on the interval

is continuous on

and differentiable o

which satisfies the conclusion of the Mean Value Theorem for

.

Enter the exact value of

, in Maple syntax, in the box below.



You may copy and paste x^4-20*x^3+154*x^2-540*x+625 into your Maple window for calculation. Copy the answer you got from Maple and paste it in the answer area. Use preview to make sure that you have copied the answer correctly.



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is the solution of

That is the real root of

.

The answer is

Suppose that

and

(a) Enter the projection of box below.

on

.

, in Maple syntax, in the

 Note : (i) In Maple syntax, a vector can be entered as

(ii)

.

(iii) In the package LinearAlgebra, the Maple comand of the dot product of u and v is u.v (b) Find the shortest distance from the point to the line . Enter the exact value of your answer in the box below.





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(a)

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.

(b) Note that the line passes through the origin. The shortest distance is the length of the vector .

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Enter the matrix

. To prevent typing errors you may copy and paste following Maple command for entering A . A := Matrix([[6, 8, 1, 2, 4, 3, 4, 2, 8, 5, 6], [7, 1, 6, 1, 7, 1, 6, 5, 7, 5, 7], [1, 6, 4, 8, 7, 8, 9, 4, 6, 3, 8], [5,



2, 1, 1, 6, 8, 4, 5, 4, 5, 8], [5, 8, 6, 8, 1, 5, 6, 4, 5, 1, 4], [8, 7, 7, 8, 9, 9, 6, 5, 1, 7, 5], [8, 8, 8, 6, 2, 9, 6, 4, 3, 3, 8], [3, 9, 8, 1, 3, 4, 5, 8, 7, 3, 6], [1, 2, 9, 2, 7, 9, 9, 4, 9, 6, 4], [6, 7, 2, 6, 6, 6, 3, 1, 4, 3, 7]]); [Note that Maple does not display the full matrix when it has more than 10 rows or 10 columns. However, you can still work with the matrix using Maple commands.] Use Maple to create the vector b that is column 4 from A and the matrix C that is made from columns 1 to 3 and 5 to 11 of A (in the same order as the columns of A). Now solve the matrix equation Cx =b and enter the 9th component of the unique vector solution for x in the box below. (Your answer should be an exact fraction, not a decimal.)

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