o #section 4.2 plot(x^3-3x^2+1.5x-14,x=-2..3); x...

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#Section 4.2

plot(x^3-3*x^2+1.5*x-14,x=-2..3);

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#When Maple is asked to solve an expression, it assumes the expression is equal to zero and will solve for all variables within the expression.

solve (3*x^2-6*x+1.5,x);1.707106781, 0.2928932188

#Note that when there is a decimal point in the expression, Maple returns an answer in decimal form. If we use an exact expression instead of the decimal, we get an exact answer.

solve (3*x^2-6*x+3/2,x);

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plot((1/3)*x^3+x,x=-5..5);

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plot((1/3)*x^3-x,x=-5..5);

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plot((1/3)*x^3-x,x=-3..3);

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plot(1/(x-1),x=-3..3,y=-10..10);

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plot(1/(x^2-1),x=-3..3,y=-10..10);

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#The following are the graphs of the derivative and the originalfunction for the in-class exercise for section 4.2.

plot( [0.05*(x - 1)*(x + 0.5)*(x - 2.5)^2*(x - 10), int(0.05*(x - 1)*(x + 0.5)*(x - 2.5)^2*(x - 10),x)], x=0..3, color=[red,blue] );

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#Section 4.3

plot(2*x^3-9*x^2+12*x-5,x=-1..3.5);

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plot(6*x^2-18*x+12,x=-1..3.5);

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plot(12*x-18,x=-1..3.5);

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plot(x*exp(-x^2/2),x=-3..3);

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plot([x*exp(-x^2/2),diff(x*exp(-x^2/2),x)],x=-3..3);

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plot([x*exp(-x^2/2),diff(x*exp(-x^2/2),x),diff(x*exp(-x^2/2),x,x)],x=-3..3,color=[red,green,blue]);

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#The following is for problem 44 p. 288

plot( [((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)), diff( ((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)), x), diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x)], x=-3..3,color=[red,green,blue]);

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solve(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x));RootOf 3 _Z9C 3 _Z8C 36 _Z7K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2K 744 _Z

C 236, index= 1 , RootOf 3 _Z9C 3 _Z8C 36 _Z7K 7 _Z6C 81 _Z5C 21 _Z4

K 278 _Z3C 195 _Z2K 744 _ZC 236, index= 2 , RootOf 3 _Z9C 3 _Z8C 36 _Z7

K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2K 744 _ZC 236, index= 3 ,

RootOf 3 _Z9C 3 _Z8C 36 _Z7K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2

K 744 _ZC 236, index= 4 , RootOf 3 _Z9C 3 _Z8C 36 _Z7K 7 _Z6C 81 _Z5C 21 _Z4






K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2K 744 _ZC 236, index= 9#Maple attempts to find exact solutions and when the solutions

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are too complex, Maple expresses the result as root of an expression.

solve(x^3+x^2+x);

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solve(x^2+y^2=1);

x = 1K y2 , y = y , x =K 1K y2 , y = ysolve(x^2+y^2=1,x);

1K y2 , K 1K y2

#We can get an approximate solution to the above problem using evalf() command.












K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2K 744 _ZC 236, index= 9

evalf(%);0.3332909936, 1.481579821, 0.4942543036C 1.835972781 I, K0.06544908310

C 1.528515490 I, K0.9455790709C 3.110493830 I, K1.781323114, K0.9455790709K 3.110493830 I, K0.06544908310K 1.528515490 I, 0.4942543036K 1.835972781 I#Other method is to use fsolve which finds solutions numerically. Problem here is that it only finds one solution ata time. Therefore, we need to tell Maple where to look for the solution. From the plot of the function, we see there should be3 solutions.

plot(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x),x=-3..3);

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fsolve(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x));K1.781323114

fsolve(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x),x,0..1);0.3332909936

fsolve(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x),x,1..2);1.481579821

#We have now found all 3 solutions accurate to 10 digits and we could have Maple display more digits if desired.

evalf(fsolve(diff(((x+1)^3*(x^2+5))/((x^3+1)*(x^2+4)),x, x),x,1..2),20);

1.4815798212751903434





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K 7 _Z6C 81 _Z5C 21 _Z4K 278 _Z3C 195 _Z2K 744 _ZC 236, index= 9

evalf(%,20);0.33329099355621728187, 1.4815798212751903434, 0.49425430357034888449

C 1.8359727813044462529 I, K0.065449083098015133147C 1.5285154895083324747 I, K0.94557907089461272448C 3.1104938302208671135 I,K1.7813231139868496790, K0.94557907089461272448K 3.1104938302208671135 I,K0.065449083098015133147K 1.5285154895083324747 I, 0.49425430357034888449K 1.8359727813044462529 I

#Activity 4.3 Equations

#Graph 1

plot(.2*(x^2*(x-1)*(x+1)*(x-2)*(x+2)+5),x=-2..2,y=-1..2);

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#Graph 2

plot((x+.5)^2*(x-.5)*(x-1.7)+.2,x=-1..2,y=-1..1);

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#Graph 3.

plot(0.3*exp(x),x=-2.5..1.5,y=-0.8..1);

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#Graph 4.

plot([x^(1/3),-(-x)^(1/3)],x=-5..5,y=-2..2,color=[red,red]);

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#Graph 5.

plot(-abs(1/x)+1,x=-2.5..2.5,y=-0.7..1.5);

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#Graph 6.

plot(exp(-x^2/2),x=-2.5..2.5,y=-0.5..1.5);

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#Section 4.4

plot((x+1)^5*sin(x-3),x=-3..0,y=-10..10);

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solve(diff((x+1)^5*sin(x-3),x));K1, K1, K1, K1, 3CRootOf _ZC 5 tan _Z C 4

evalf(solve(diff((x+1)^5*sin(x-3),x)));K1., K1., K1., K1., 2.402483740

#Clearly the solve command did not find all the solutions. The graph helps us know that there must be additional solutions in the interval besides x = -1

fsolve(diff((x+1)^5*sin(x-3),x));K.2838542552

fsolve(diff((x+1)^5*sin(x-3),x),x=-1.5..-0.29);K.9999999964

#This looks a lot like x = -1, but we must make that interpretation.

fsolve(diff((x+1)^5*sin(x-3),x),x=-3..-2.5);K2.917060175

plot(diff((x+1)^5*sin(x-3),x),x=-3..0);

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#We can take a closer look around y = 0.

plot(diff((x+1)^5*sin(x-3),x),x=-3..0,y=-0.5..0.5);

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plot(diff((x+1)^5*sin(x-3),x),x=-3..0,y=-0.1..0.1, numpoints=2000);

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plot(diff((x+1)^5*sin(x-3),x),x=-3..0,y=-0.01..0.01, numpoints =2000);

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plot([1/(x^2+4*x+3),1/(x^2+4*x+4),1/(x^2+4*x+5)],x=-5..3,y=-3..3,color=[red,green,blue]);

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plot([1/(x^2+4*x+4),1/(x^2+4*x+5),1/(x^2+4*x+6)],x=-5..3,y=-1..1,color=[red,green,blue]);

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plot((10*x*(x-1)^4)/((x-2)^3*(x+1)^2),x=-5..5,y=-5..25);

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plot((10*x*(x-1)^4)/((x-2)^3*(x+1)^2),x=-1..3,y=-1..1);

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plot(diff((10*x*(x-1)^4)/((x-2)^3*(x+1)^2),x),x=-5..5,y=-5..5);

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plot(diff((10*x*(x-1)^4)/((x-2)^3*(x+1)^2),x),x=-5..5,y=-5..5,numpoints=2000);

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#Note that the following is the syntax for parametric plots. Also note that the command scaling=constrained forces a 1-1 or square plot.

plot([sin(2*t),sin(3*t),t=0..2*Pi],x=-1..1,y=-1..1,scaling=constrained);

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Section 4.9

A slopefield can be created in Maple using the dfieldplot routine from the DEtools package. Note that what we are saying in this input is that we have a derivative of y(x) with respect to x which is equal to afunction, in this case exp(x^2/2), and that what is being plotted is y(x).

with(DEtools);AreSimilar, DEnormal, DEplot, DEplot3d, DEplot_polygon, DFactor, DFactorLCLM,

DFactorsols, Dchangevar, FunctionDecomposition, GCRD, Gosper, Heunsols,

Homomorphisms, IsHyperexponential, LCLM, MeijerGsols, MultiplicativeDecomposition,

PDEchangecoords, PolynomialNormalForm, RationalCanonicalForm, ReduceHyperexp,

RiemannPsols, Xchange, Xcommutator, Xgauge, Zeilberger, abelsol, adjoint, autonomous,

bernoullisol, buildsol, buildsym, canoni, caseplot, casesplit, checkrank, chinisol, clairautsol,

constcoeffsols, convertAlg, convertsys, dalembertsol, dcoeffs, de2diffop, dfieldplot,

diff_table, diffop2de, dperiodic_sols, dpolyform, dsubs, eigenring, endomorphism_charpoly,

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equinv, hk, eulersols, exactsol, expsols, exterior_power, firint, firtest, formal_sol, gen_exp,

generate_ic, genhomosol, gensys, hamilton_eqs, hypergeomsols, hyperode, indicialeq,

infgen, initialdata, integrate_sols, intfactor, invariants, kovacicsols, leftdivision, liesol,

line_int, linearsol, matrixDE, matrix_riccati, maxdimsystems, moser_reduce, muchange,

mult, mutest, newton_polygon, normalG2, ode_int_y, ode_y1, odeadvisor, odepde,

parametricsol, particularsol, phaseportrait, poincare, polysols, power_equivalent, ratsols,

redode, reduceOrder, reduce_order, regular_parts, regularsp, remove_RootOf,

riccati_system, riccatisol, rifread, rifsimp, rightdivision, rtaylor, separablesol, singularities,

solve_group, super_reduce, symgen, symmetric_power, symmetric_product, symtest,

transinv, translate, untranslate, varparam, zoomdfieldplot(diff(y(x),x)=exp(x^2/2),y(x),x=-2..2,y=-2..2);

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o #section 4.2 plot(x^3-3*x^2+1.5*x-14,x=-2..3); x...

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o #section 4.2 plot(x^3-3x^2+1.5x-14,x=-2..3); x...