<Text-field style="Heading 1" layout="Heading 1">Question 1 [4 points] (Differentiation and Tangent Lines

TDEC 160: Maple Quiz

Jeremy Johnson

Name:

Section:

Instructions: There are three questions, each worth 4 points, for a total of 12 points (partial credit will be given). The quiz must be completed in 50 minutes and submitted to webct. Please put your name and section in the worksheet above.

The quiz must be done independently using Maple. You can use all of the available help resources in Maple, but nothing else. If you have any questions, you may ask for clarification. Questions have multiple parts and you should attempt all parts. Make sure you read the instructions carefully. If you have forgotten how to use a command, use Maple's help facility.

<Text-field style="Heading 1" layout="Heading 1">Question 1 [4 points] (Differentiation and Tangent Lines - diff, evalf, and plot)</Text-field>

In this question you will investigate the functions 2^x and 3^x. In particular, you will compute the slope of these functions (use diff) at the point x=0 (also use evalf to compute numeric values of the slopes). The you will plot, in, in two separte plots, the function 2^x and the line tangent to 2^x at the point x=0, and the function 3^x and the line tangent to 3^x at the point x=0. Finally use the command display to combin the two plots.

with(plots);

Warning, the name changecoords has been redefined

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d2 := diff(2^x,x);

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p0 := subs(x=0,d2);

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evalf(p0);

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

plot({2^x,1+log(2)*x},x=-2..2);

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

plot1 := %;

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

d3 := diff(3^x,x);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USNkM0YoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y4LyUqc3Vic2NyaXB0R0Y4LyUsc3VwZXJzY3JpcHRHRjgvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGNS1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGW3AvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUwZm9udF9zdHlsZV9uYW1lR0ZYLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHRkQvJStiYWNrZ3JvdW5kR0ZHLUYkNiUtSSVtc3VwR0YlNiUtSSNtbkdGJTY5USIzRihGMEYzRjYvRjpGOEY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ24vRmpuUSdub3JtYWxGKEZcby1GLTY5USJ4RihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYoLUZfbzYzUTEmSW52aXNpYmxlVGltZXM7RihGYm9GZW9GZ28vRmpvUSQwZW1GKC9GXXBGXHNGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRiQ2JS1GLTY5USNsbkYoRjBGM0Y2Rl9yRjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZgckZcby1GX282M1EwJkFwcGx5RnVuY3Rpb247RihGYm9GZW9GZ29GW3NGXXNGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRiQ2JS1GX282M1EiKEYoL0Zjb1EncHJlZml4RigvRmZvRjtGZ28vRmpvUS50aGlubWF0aHNwYWNlRigvRl1wRl90L0ZfcEY7RmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiNGW3ItRl9vNjNRIilGKC9GY29RKHBvc3RmaXhGKEZddEZnb0ZedC9GXXBRMnZlcnl0aGlubWF0aHNwYWNlRihGYXRGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHE3Iy1fRilJLG1wcmludHNsYXNoR0YoNiQ3Iz5JI2QzR0YoKiYpIiIkSSJ4R0YoIiIiLUkjbG5HNiQlKnByb3RlY3RlZEdGKjYjRmV1Rmd1NyNGY3U=

p1 := subs(x=0,d3);

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

evalf(p1);

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

plot({3^x,1+log(3)*x},x=-2..2);

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

plot2 := %;

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

display({plot1,plot2});

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

<Text-field style="Heading 1" layout="Heading 1">Question 2 [4 points] (The Definition of the Derivative - limit, seq, evalf, and solve)</Text-field>

In this question you will investigate the derivative of the function a^x.

1) Use the limit command to determinate the derivative of 2^x by definition (i.e. 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). Check the answer returned by limit using diff.

2) Use the formula obtained in (1) to compute the value of the derivative at x=0. Use evalf to get a numeric approximation.

3) Numerically compute the value of the derivative of 2^x at x=0 using the definition of the derivative. Compute a sequence of values using 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How do these values compare to the result from (2)?

4) Use diff to find the derivative of 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 .

5) Use solve to find the value of 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such that 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

diff(2^x,x);

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

limit((2^(x+h)-2^x)/h,h=0);

seq(evalf((2^(10^(-h))-1)/(10^(-h))),h=0..10);

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

limit((2^h-1)/h,h=0);

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

evalf(%);

diff(a^x,x);

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solve(ln(a)=1);

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<Text-field style="Heading 1" layout="Heading 1">Question 3 [4 points] (Recursion and Trees) </Text-field>

In this question you will write a recursive Maple function to compute the number of nodes in a binary expression tree. Trees will be represented as they were in Lab 5 and the code to build and manipulate trees is provided in the subsection "Expression Tree Code".

First evaluate the expression tree code so that the provided routines are available in your Maple session. Second evaluate the expression that constructs the tree T and print it using the provided PrintTree function and evaluate it using the provided EvalTree function. Differentiate the tree T, with the provided DiffTree function, and check, using diff and EvalTree that the computed derivative is correct.

Next write a recursive Maple function called NumberNodes, which computes the number of nodes in an expression tree. See below for a few hints on how to do and check this.

Use your function to compute the number of nodes in the tree T (it should be 9) and the number of nodes in the tree returned by DiffTree with T as an input.

<Text-field style="Heading 2" layout="Heading 2">Expression Tree Code</Text-field>

MakeTree := proc(val,left,right)

return [val,left,right];

end;

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NullTree := proc()

return [];

end;

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IsNullTree := proc(T)

return T = NullTree();

end;

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MakeLeaf := proc(val)

return [val,NullTree(),NullTree()];

end;

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USlNYWtlTGVhZkYoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y4LyUqc3Vic2NyaXB0R0Y4LyUsc3VwZXJzY3JpcHRHRjgvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGNS1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGW3AvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUwZm9udF9zdHlsZV9uYW1lR0ZYLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHRkQvJStiYWNrZ3JvdW5kR0ZHLUYkNigtRl9vNjNRJXByb2NGKC9GY29RIUYoRmVvRmdvL0Zqb1EkMGVtRigvRl1wRl5yRl5wRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiUtRl9vNjNRIihGKC9GY29RJ3ByZWZpeEYoL0Zmb0Y7RmdvL0Zqb1EudGhpbm1hdGhzcGFjZUYoL0ZdcEZpci9GX3BGO0ZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYjLUYtNjlRJHZhbEYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZfbzYzUSIpRigvRmNvUShwb3N0Zml4RihGZ3JGZ29GaHIvRl1wUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRltzRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUknbXNwYWNlR0YlNiYvJSdoZWlnaHRHUScwLjB+ZXhGKC8lJndpZHRoR1EnMC4zfmVtRigvJSZkZXB0aEdGXXQvJSpsaW5lYnJlYWtHUTFmaXJzdHByb2NuZXdsaW5lRigtRiQ2JC1GX282M1EncmV0dXJuRihGW3JGZW9GZ29GXXIvRl1wUTBtZWRpdW1tYXRoc3BhY2VGKEZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYlLUZfbzYzUSJbRihGZXJGZ3JGZ29GaHJGanJGW3NGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRiQ2J0Zecy1GX282M1EiLEYoRmJvRmVvL0Zob0Y7Rl1yL0ZdcFEzdmVyeXRoaWNrbWF0aHNwYWNlRihGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRiQ2JS1GLTY5USlOdWxsVHJlZUYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZfbzYzUTAmQXBwbHlGdW5jdGlvbjtGKEZib0Zlb0Znb0ZdckZfckZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYlRmJyLUYkNiMtRi02OUZcckYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcb0Zhc0ZkdUZqdS1GX282M1EiXUYoRmRzRmdyRmdvRmhyRmZzRltzRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUZpczYmRlt0L0ZfdFEnMC4wfmVtRihGYXQvRmR0UTZkZWNyZWFzZWluZGVudG5ld2xpbmVGKC1GX282M1EpZW5kfnByb2NGKEZbckZlb0Znby9Gam9GXHVGX3JGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHE3Iy1fRilJLG1wcmludHNsYXNoR0YoNiQ3Iz5JKU1ha2VMZWFmR0YoZio2I0kkdmFsR0YoRihGKEYoTzclRl94LUkpTnVsbFRyZWVHRihGKEZieEYoRihGKDcjRl14

GetLeft := proc(T)

return T[2];

end;

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

GetRight := proc(T)

return T[3];

end;

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

GetVal := proc(T)

return T[1];

end;

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

The following function prints a tree in a human readable form. To simplify the code, the tree is printed sideways, i.e. rotated 90 degrees counter clockwise.

# A function to print a binary tree. # The root of the tree is printed to the left and the tree should be rotated to be viewed. PrintTree := proc(T)

PrintTreeAux(T,"");

end;

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PrintTreeAux := proc(T,str) local leadingblanks; leadingblanks := " ";

if IsNullTree(T) then

return;

else

PrintTreeAux(GetRight(T),cat(leadingblanks,str)); # Print right child with additional indentation

printf("%s %a\n",str,GetVal(T));

PrintTreeAux(GetLeft(T),cat(leadingblanks,str));

end if;

end;

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EvalTree := proc(T)

local val,left,right; if IsNullTree(T) then return; end;

val := GetVal(T); left := GetLeft(T); right := GetRight(T);

if (val = `+`) then

return `+`(EvalTree(left),EvalTree(right));

elif (val = `-`) then

return `-`(EvalTree(left),EvalTree(right));

elif (val = `*`) then

return `*`(EvalTree(left),EvalTree(right));

elif (val = `/`) then