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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 54 "Click on a box with a + inside to
 expland the section." }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 6 "Limits" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "limit((x+2)^(1/ln(x)),x=inf
inity);" }{TEXT -1 39 " Evaluate a limit, exactly if possible." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "limit((x^2+3*x)/(4*x^2-3e^(-
x)), x=infinity);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Derivative
s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x-> 5*x^2+1; " }
{TEXT -1 56 "Define the function f to be the map taking x to 5*x^2+1.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "D(f); " }{TEXT -1 71 "ta
ke the derivative of the function f.  The answer is another function.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "D(D(f)); " }{TEXT -1 29 
"Derivative of the derivative." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 2 "f;" }{TEXT -1 52 " This is not a good way to see what the funct
ion is." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }{TEXT -1 
44 " Evaluate f at x to see what function it is." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 14 "diff(f(x),x); " }{TEXT -1 38 "Take the deriva
tive of the expression " }{TEXT 256 4 "f(x)" }{TEXT -1 17 " with respe
ct to " }{TEXT 257 1 "x" }{TEXT -1 47 ".  The answer is an expression,
 not a function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:=unap
ply(10*x,x); " }{TEXT -1 35 "Turn an expression into a function." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(2);  " }{TEXT -1 28 "Evalua
te the function g at 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "u
napply(f(x),x); " }{TEXT -1 20 "Turn the expression " }{TEXT 258 4 "f(
x)" }{TEXT -1 63 " into a function.  This is another way of seeing wha
t function " }{TEXT 259 1 "f" }{TEXT -1 4 " is." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 35 "diff((x^2-3*x^4)/(ln(x)+x^(-3)),x);" }{TEXT 
-1 16 " Just for kicks!" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Anti
derivatives" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "F:=x->int(f(t
),t=1..x); " }{TEXT -1 21 "An antiderivative of " }{TEXT 260 1 "f" }
{TEXT -1 47 ", a Maple function.  The variable t is a dummy." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(x);" }{TEXT -1 43 " Evaluat
e F at x to see what function it is" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "P:=x->int((sin^2)(x)*cos(x),x); " }{TEXT -1 54 "The f
unction P is the antiderivative of an expression." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 6 "P(x); " }{TEXT -1 34 "See explicitly what fun
ction P is." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Q:=int((sin^
4)(x)*cos(x),x); " }{TEXT -1 56 "The expression Q is the antiderivativ
e of an expression." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "Q(2);
" }{TEXT -1 84 " Q is an expression, not a function, so this does not \+
produce what you might expect!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "unapply(Q,x)(2);" }{TEXT -1 66 "This is better.  First turn Q \+
into a function, then evaluate at 2." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "evalf(%); " }{TEXT -1 21 "Evaluate numerically." }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "Definite Integrals" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int(f(x),x=1..5); " }{TEXT -1 39 "E
valuate the definite integral exactly." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "int(exp(-x^3),x=1..5); " }{TEXT -1 72 "There is no cl
osed form expression for this integral, so Maple gives up." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Int(exp(-x^3),x=1..5); " }{TEXT -1 
41 "Set up, but do not evaluate the integral." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "evalf(%); " }{TEXT -1 34 "Evaluate the integral \+
numerically." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 36 "Rectangles unde
r graphs of functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }{TEXT -1 25 " Load the p
ackage called " }{TEXT 261 7 "student" }{TEXT -1 61 ".  The output lis
ts the functions included in this package.  " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "with(student): " }{TEXT -1 59 "Use a colon rathe
r than a semicolon to suppress the output." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "f:=x->9-x^2; " }{TEXT -1 18 "Define a function." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rightbox(f(x),x=1..6,20); \+
" }{TEXT -1 66 "Plot the function together with 20 right-hand endpoint
 rectangles." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rightsum(f(
x),x=1..6,20); " }{TEXT -1 75 "Set up the Riemann sum corresponding to
 the total area of these rectangles." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "value(%); " }{TEXT -1 48 "Give the exact value of the
 previous expression." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "R:
=[[n,rightsum(f(x),x=1..6,n)] $n=2..60]: " }{TEXT -1 47 "Set up the Ri
emann sum for an arbitrary number " }{TEXT 262 1 "n" }{TEXT -1 35 " of
 right-hand endpoint rectangles." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "plot(R,x=2..60,style=point,symbol=circle);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "L:=[[n,leftsum(f(x),x=1..6,n
)] $n=2..60]: " }{TEXT -1 47 "Set up the Riemann sum for an arbitrary \+
number " }{TEXT 263 1 "n" }{TEXT -1 34 " of left-hand endpoint rectang
les." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(L,x=2..60,styl
e=point,symbol=circle);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
T:=(L+R)/2: " }{TEXT -1 57 "The trapezoidal rule is supposed to conver
ge more quickly" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(T,x
=2..60,style=point,symbol=circle);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "int(f(x),x=1..6); " }{TEXT -1 34 "Confirm the value o
f the integral." }}}}}{MARK "1 1 0 0" 5 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }