{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 1 1 2 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 276 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1 " 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 4" 5 20 1 {CSTYLE "" -1 -1 "" 1 10 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 1 2 0 1 }} {SECT 0 {SECT 0 {PARA 256 "" 0 "" {TEXT 259 55 "Section 5: Functions: \+ Defining, Evaluating and Graphing" }}{PARA 0 "" 0 "" {TEXT -1 186 "In \+ this section you will learn how to define a function f(x) in Maple. Th e remainder of the section covers evaluating functions, solving equati ons with functions, and graphing functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 41 "Defining and Clearing a Function in Map le" }}{PARA 0 "" 0 "" {TEXT -1 138 "To distinguish a function from an \+ expression, Maple requires special notation when defining a function. \+ For example, the function f(x) = " }{XPPEDIT 18 0 "cos (Pi*x) + 3" "6 #,&-%$cosG6#*&%#PiG\"\"\"%\"xGF)F)\"\"$F)" }{TEXT -1 15 " is defined a s:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=x->cos(Pi*x)+3; \+ " }}}{PARA 0 "" 0 "" {TEXT -1 36 "Take note of the syntax here. It is \+ " }{TEXT 257 10 "absolutely" }{TEXT -1 97 " necessary to type the \"ar row\" - > made by typing a \"minus sign\" and a \"greater than\" sy mbol. " }{TEXT 256 44 "Maple will not define a function if you type" } {TEXT -1 22 " f(x):=cos(Pi*x)+3 ;" }{TEXT 262 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 128 "Below is a comparison of an expression and a function. Note the difference in syntax and h ow Maple returns the output for each." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "y:=(x + 2)/(x^3 + 5*x + 2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f:=x->(x + 2)/(x^3 + 5*x + 2);" }}}{PARA 0 "" 0 "" {TEXT -1 188 "Functions always require an arrow when typing in; Map le should also have an arrow in its output. Always check the output f or the arrow to confirm that you have in fact defined a function." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 260 12 " Exercise 5.1" }}{PARA 0 "" 0 "" {TEXT -1 26 "Enter the function h(x) = " }{XPPEDIT 18 0 "x^3*sin(2*x+1)" "6#*&%\"xG\"\"$-%$sinG6#,&*&\"\"#\" \"\"F$F,F,F,F,F," }{TEXT -1 26 " in the workspace below. " }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 5.1" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 " " 0 "" {TEXT -1 10 "Answer 5.1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "h:= x-> x^3*sin(2*x+1);" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 283 "Once you have defined a function, Maple \+ will remember that function during your entire working session. If yo u want to overwrite the function with a new definition, you simply ret ype the definition. For example, if you want to replace the function \+ f(x) above with ln(cos 5x), type:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=x->ln(cos(5*x));" }}}{PARA 0 "" 0 "" {TEXT -1 57 " We can confirm the current value for the function f(x) :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "If you want to clear the function \+ f(x) without redefining it, type:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:='f';" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 121 "It's always a good idea to clear your functions w hen you start a new problem. Alternatively you can use restart to clea r " }{TEXT 279 10 "everything" }{TEXT -1 13 " from memory." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Evaluati ng a Function" }}{PARA 0 "" 0 "" {TEXT -1 209 "Once a function has bee n defined, you can evaluate it at various values or literal expression s using function notation. It's always a good idea to clear the funct ion name first before entering a new function." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:='f';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->3*x+x^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(-1 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f(2+sqrt(5));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(f(2+sqrt(5)));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(x+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(f(x+h)-f(x))/h;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 73 "If more than one function is involved, co mposing functions is easy to do." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g:=x->cos(x)+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " f(g(Pi/3));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "j:=x->g(f(x) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "j(x);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 261 12 "Exercise 5. 2" }}{PARA 0 "" 0 "" {TEXT -1 33 "Exercise 2 : Define the function " } {XPPEDIT 18 0 "s(t)= (3+t^2)/sqrt(3*t+1)" "6#/-%\"sG6#%\"tG*&,&\"\"$\" \"\"*$F'\"\"#F+F+-%%sqrtG6#,&*&F*F+F'F+F+F+F+!\"\"" }{TEXT -1 27 " th en have Maple calculate" }}{PARA 0 "" 0 "" {TEXT -1 91 "s(2),and s(t-3 ) and s(t) - s(3) and simplify your results. Don't forget the arrow no tation!" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 5.2 " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 10 "Answer 5. 2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "s:= t-> (3 + t^2)/(sqrt (3*t+1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s(2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "s(t - 3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify (%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s(t) - s(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 136 "Notice that if you define a function, there is no nee d to evaluate the function using the \"subs\" command like you do with expressions. " }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 37 "Solving Equat ions involving Functions" }}{PARA 0 "" 0 "" {TEXT -1 102 "Once your fu nction is defined, you can solve equations with functions either exact ly or approximately:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g:='g ';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g:=t->t^3-6*t^2+6*t+8 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(g(t)=0,t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(g(t)=0,t);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Graphi ng a Function" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 258 4 "plot " }{TEXT -1 39 " function works the same for functions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h:='h'; y:='y'; x:='x';" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "h:=x->x*exp(-x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(h(x),x=-1..4,y=-2..1);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Several f unctions can be graphed simultaneously just at we did for expressions. " }}{PARA 0 "" 0 "" {TEXT -1 24 "Consider the function " }{XPPEDIT 18 0 "f(x) =4/(x^2+1)" "6#/-%\"fG6#%\"xG*&\"\"%\"\"\",&*$F'\"\"#F*F*F* !\"\"" }{TEXT -1 65 ". Below we graph this function along with the ho rizontal shifts " }{XPPEDIT 18 0 "f(x+1)" "6#-%\"fG6#,&%\"xG\"\"\"F(F( " }{TEXT -1 3 " , " }{XPPEDIT 18 0 "f(x-3) " "6#-%\"fG6#,&%\"xG\"\"\" \"\"$!\"\"" }{TEXT -1 4 "and " }{XPPEDIT 18 0 "f(x-6)" "6#-%\"fG6#,&% \"xG\"\"\"\"\"'!\"\"" }{TEXT -1 26 " . Can you identify each ?" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->2/(x^2+1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plo t([f(x),f(x+1),f(x-3),f(x-6)],x=-5..10,y=-1..3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 264 12 "Exercise 5.3" } }{PARA 0 "" 0 "" {TEXT 263 21 "Define the function " }{XPPEDIT 18 0 " f(x)=2*x-abs(x^2-5)" "6#/-%\"fG6#%\"xG,&*&\"\"#\"\"\"F'F+F+-%$absG6#,& *$F'F*F+\"\"&!\"\"F2" }{TEXT -1 38 " then answer the following questi ons." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "a ) Find the value of f(6.5) " }}{PARA 0 "" 0 "" {TEXT -1 55 "b) Simpli fy the expression f(z-4) where z is a variable" }}{PARA 0 "" 0 "" {TEXT -1 24 "c) Plot a graph of f(x) " }}{PARA 0 "" 0 "" {TEXT -1 42 " d) Find all values of x such that f(x)=0. " }}{SECT 1 {PARA 20 "" 0 " " {TEXT 265 21 "Student Workspace 5.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 20 "" 0 " " {TEXT 266 10 "Answer 5.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=x->2*x-abs(x^2-5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(6.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(f(z-4) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plot(f(x),x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(f(x)=0,x=0..2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(f(x)=0,x=3..4);" }}}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 268 12 "Exercise 5.4" }}{PARA 0 "" 0 " " {TEXT 267 22 "Define the functions " }{XPPEDIT 18 0 "g(x)= 5*exp(-0 .5*x)" "6#/-%\"gG6#%\"xG*&\"\"&\"\"\"-%$expG6#,$*&$F)!\"\"F*F'F*F1F*" }{TEXT 275 7 " and " }{XPPEDIT 18 0 "h(x)=x+1" "6#/-%\"hG6#%\"xG,&F' \"\"\"F)F)" }{TEXT 276 24 " then do the following." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "a) Plot a graph that s hows both functions g(x) and h(x). Experiment with different values fo r domain and range." }}{PARA 0 "" 0 "" {TEXT -1 110 "b) Estimate the c oordinates of the point of intersection of these two graphs by using l eft mouse-button click." }}{PARA 0 "" 0 "" {TEXT -1 7 "c) Use " } {TEXT 278 9 "fsolve( )" }{TEXT -1 108 " to solve the equation g(x)=h(x ). How does the solution of this equation relate to your answer to par t (b). " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 269 21 "Student Work space 5.4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 20 "" 0 "" {TEXT 270 10 "Answer 5.4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:=x->5*exp(-0.5*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "h:=x->x+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot([g(x),h(x)],x=-5..5,y=-20..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot([g(x),h(x)],x=1..2,y=1..4);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "xval:=fsolve(g(x)=h(x),x); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 202 "The solution to g(x)=h(x) is the x-coordinate of the point of intersection of g(x) and h(x). To fi nd the corresponding y-coordinate of the intersection point evaluate e ither g(x) or h(x) at this value. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g(xval);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " h(xval);" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 272 12 "Exercise 5.5" }} {PARA 0 "" 0 "" {TEXT 271 20 "Define the function " }{XPPEDIT 18 0 "k( x)=x+3*sin(2*x)" "6#/-%\"kG6#%\"xG,&F'\"\"\"*&\"\"$F)-%$sinG6#*&\"\"#F )F'F)F)F)" }{TEXT -1 25 " , then do the following:" }}{PARA 0 "" 0 "" {TEXT -1 58 "a) Plot the graph of this function on the domain [-1,8] . " }}{PARA 0 "" 0 "" {TEXT -1 158 "b) Modify your plot from part (a) t o include the horizontal line y=4. Use this new plot to estimate the n umber and approximate values for x such that k(x)=4." }}{PARA 0 "" 0 "" {TEXT -1 8 "c) What " }{TEXT 277 6 "single" }{TEXT -1 83 " function could you graph that would give you the same information as in part ( b) " }}{PARA 0 "" 0 "" {TEXT -1 86 "d) Use Maple's fsolve( ) command \+ to approximate all solutions to the equation k(x)=4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 273 21 "Student Work space 5.5" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 20 "" 0 " " {TEXT 274 10 "Answer 5.5" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 " a) \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "k:=x->x+3*sin(2*x);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(k(x),x=-1..8);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot([k(x),4],x=-1..8);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "There appears to be three intersection points at x=3.25 , 4.825 and 5.95 . " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "c) We could graph k(x) - 4 and lo ok for x-intercepts. These will correspond to x-values found in part ( b)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(k(x)-4,x=-1..8) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Here are the solutions using fsolve( ) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(k(x) =4,x=2 .. 3.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(k (x)=4,x=3.5 .. 5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fsolv e(k(x)=4,x=5 .. 7);" }}}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }