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A„€ž  6ˆ-Œ Ai  ¼ 4ÑA„@Æ 06—-@:Ñ,&@d6–-„8—,0—$²"„8Œ,A„`Ð  6„8—,-Œ(–A„0Ú @ 6€-Œ6ˆ-– A0'‚-@&0–„8‚,@6„8‚,-„8‚,&€%Œä  ‚î 6Ð-Œø  A44±A‚ ! A‚0 !(–6Œ-Œ& A„@! 6„8—,-Ž A„ ! 6ˆ-Æ!!'6ˆ-ˆ%ˆ ÐA„"!> ˆ-º   ˆ ýÞ4 ERROR, expected > A‚4!?!„8Œ,)@ „8Œ,56.existing topic number? A„€>!p >:A%,p„8Œ,A† A‡A‡@A‡–AˆAˆAˆ"Aˆ&Aˆ4AˆFAˆ`f!V' >:A%,Help is available on* V &1: Expressions 7: Compound Linesg!P' 2: Algebraic Expand 8: QuotingP $3: Functions 9: ReEvaluationh!b* "4: More Expansion 10: DerivativeO  5: Assignments 11: Integralb 6: Non-displayi!A > 3Enter a topic number followed by a question markA j!T, $Study topics in order the first time/ J See manual for detailsT A‚ ¬!QQ IAfter each question mark prompt, enteran expression using digits, decimal¶!T(  points, parentheses and 1-letterT &variables together with operators +, -À!SS K/, * and ^. The latter means raising to a power. *, meaning multiply, canÊ!UU Lbe omitted. Following each such inputan equivalent expression is displayed,Ô!K) !derived by reordering, collectingK similar terms, and other mildÞ![+ #transformations. As examples, type. H 3 X^2 Y + 5 (XYX - 7)[ (A^2*B)^.5 / Aè! Aü!N& Type < to turn on expansion ofN #positive integer powers of sums and"P) !full distribution of numerator orP "denominator factors over numerator"R' sums. Type > to turn off theseO #transformations. For example, typeR "@  <(X+Y)^2>!  <(X+Y)(X-Y)6 (X+Y)/(X-Y) + 5>@ A$"UU LExpressions can include the six radiantrig functions SIN, COS, TAN, COT, SEC."UU Land CSC, along with their first three inverses ASN, ACS and ACT. Expressions8"UU Lcan also contain the natural log and exponential functions, spelled LOG andB"RR JEXP. Parentheses can be omitted from around arguments that are constants,L"SS Kvariables, functional forms, or their negatives. Automatic transformationsV"aP Hexploit symmetry, inversion, logs of powers, and numeric arguments. Asa  Examples tryZ"E  > COS -X!  EXP LOG X/  LOG (X^2); 4 ATN 1E A\"RR JWhen ALGEBRAIC expansion is turned on via <, logs of products or quotients^"SS Kare rephrased as sums or differences of logs, and other trig functions are`"RR Jreplaced by sines and cosines. Typing[ turns on HARMONIC expansion, whichb"PP Htransforms positive integer powers andproducts of sines and cosines intod"S* "'linear combinations' of sines andS $cosines of multiple angles and anglef"ZW Osums or differences. Typing ] turns off harmonic expansion. As examples, tryZ h"W  < LOG (XY/Z)$  TAN X CSC X6  [ SIN X COS YM SINX^2 + COSX^2 ]>W Aj"> An entry of the form ;  variable = expression> l"N) !causes the resulting value of theN  expression to be ASSIGNED to then"S& variable for use in subsequentP %expressions. For example, try typingS p"4  P = 5(X+Y+Z)* P + 1/P + X LOG P4 Ar"ll dFollow an assignment with a semicolon to suppress display of an assigned value. For example, tryt"%  P = S+1; P^3% Av"RR JSeveral assignments can precede an assignment or expression in a singlex"]: 2entry, separated by semicolons. For example, try= S P=R+1; Q=L+P; Q^2] Az"QQ ITo prevent a name from contributing its value to an expression, precede|"Q(  the name by an apostrophe. ThisQ $provides a way of clearing the value~"L: 2of a variable back to its name. For example, try= L  P=L+5; P^2€"  P='P; P^2 A‚"< If we enter the line 9 H='H; P=H+1; H=2; P^2< „"PP Hthen H becomes 2 after P becomes H+1, so the displayed result is (H+1)^2†"UU Lrather than 9. However, we can followthe expression P^2 with the operator @ˆ"OL Dto RE-EVALUATE P^2 so that H therein is updated to its new value 2:O Š"d H='H; P=H+1; H=2; P^2 @" d =@ has the same precedence and left-to-right order as additionŒ" AŽ"MM ETo determine the partial derivative ofan expression with respect to a"T2 *variable, enter an expression of the form5 Q  expression % variableT ’"L(  % is named to suggest a ratio ofL infinitesimals. % has the same”"LI Aprecedence and left-to-right order as addition. As examples, tryL –"C% X='X; A='A; AX^3 + SIN X % X9 A^2 X^3 % X % AC Aœ"UU LTo determine an antiderivative of an expression with respect to a variable,ž"I' enter an expression of the form* F  expression $ variableI  "R) !$ is named to suggest an integralR $sign. $ has the same precedence and¢"PP Hleft-to-right order as addition. Avoidexpansion of integrands, which may¤"L(  mask a known integrable pattern,L because algebraic then harmonic¦"PP Hexpansion are tried automatically if the given form can't be integrated¨"^# directly. As examples, try& H X='X; A='A; 3AX^2 + COS X $ X^ COS LOG X / X $ X(#f \ QAfter entering several such examples, enter a question mark to see the help menu.f A‚ %"6.easier problem" A„€'€ D:CALCULUS