User manual HP 40GS

[. . . ] hp40g+. book Page i Friday, December 9, 2005 1:03 AM HP 40gs graphing calculator user's guide Edition1 Part Number F2225AA-90001 title. fm Page ii Friday, February 17, 2006 9:48 AM Notice REGISTER YOUR PRODUCT AT: www. register. hp. com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. © Copyright 1994-1995, 1999-2000, 2003, 2006 Hewlett-Packard Development Company, L. P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 1 April 2005 hp40g+. book Page iii Friday, December 9, 2005 1:03 AM Contents Preface Manual conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [. . . ] Typing: FACTOR(F(5)) gives: 641·6700417 Typing: F(6) gives: 18446744073709551617 Using FACTOR to factor it, then yields: 274177·67280421310721 EXPAND Distributivity EXPAND expands and simplifies an expression. Example Typing: XPAND ( ( X + 2 X + 1 ) ( X ­ 2 X + 1 ) gives: x +1 4 2 2 FACTOR Factorization FACTOR factors an expression. Example To factor: x +1 type: FACTOR(X4+1) FACTOR is located in the ALGB menu. 4 14-12 Computer Algebra System (CAS) hp40g+. book Page 13 Friday, December 9, 2005 1:03 AM In real mode, the result is: (x + 2 x + 1) (x ­ 2 x + 1) In complex mode (using CFG), the result is: 1----- ( 2x + ( 1 + i ) 2 ) ( 2x ­ ( 1 + i ) 2 ) ( 2x + ( 1 ­ i ) 2 ) 16 ( 2x ­ ( 1 ­ i ) 2 ) 2 2 PARTFRAC Partial fraction expansion PARTFRAC has a rational fraction as an argument. PARTFRAC returns the partial fraction decomposition of this rational fraction. Example To perform a partial fraction decomposition of a rational function, such as: x ­2x +1 -----------------------------------------------------------------------4 3 2 x ­ 2 x + 2 x ­ (2 x + 1) you use the PARTFRAC command. In real and direct mode, this produces: x­3 ­1 x + 2 + --------------------- + -----------------2 2x +2 2x­2 In complex mode, this produces: 1 ­ 3i ­1 1 + 3i ----------------------------4 2 4 x + 2 + ------------- + ---------- + ------------x+i x­1 x­i 5 3 QUOTE Quoted expression QUOTE(expression) is used to prevent an expression from being evaluated or simplified. Example 1 Typing: 1 im QUOTE ( ( 2X ­ 1 ) EXP( -- ­ 1 ), X = + X gives: + Computer Algebra System (CAS) 14-13 hp40g+. book Page 14 Friday, December 9, 2005 1:03 AM Example 2 Typing: SUBST(QUOTE(CONJ(Z)), Z=1+i) gives: CONJ(1+i) STORE Store an object in a variable STORE stores an object in a variable. STORE is found in the ALGB menu or the Equation Writer menu bar. Example Type: STORE(X2-4, ABC) or type: X2-4 then select it and call STORE, then type ABC, then press ENTER to confirm the definition of the variable ABC. To clear the variable, press VARS in the Equation Writer (then choose PURGE on the menu bar), or select UNASSIGN on the ALGB menu by typing, for example, UNASSIGN(ABC) | Substitute a value for a variable | is an infix operator used to substitute a value for a variable in an expression (similar to the function SUBST). | has two parameters: an expression dependent on a parameter, and an equality (parameter=substitute value). | substitutes the specified value for the variable in the expression. Typing: X ­1 X = 2 gives: 2 ­1 2 2 14-14 Computer Algebra System (CAS) hp40g+. book Page 15 Friday, December 9, 2005 1:03 AM SUBST Substitute a value for a variable SUBST has two parameters: an expression dependent on a parameter, and an equality (parameter=substitute value). SUBST substitutes the specified value for the variable in the expression. Typing: SUBST(A2+1, A=2) gives: 2 +1 2 TEXPAND Develop in terms of sine and cosine TEXPAND has a trigonometric expression or transcendental function as an argument. TEXPAND develops this expression in terms of sin(x) and cos(x). Example Typing: TEXPAND(COS(X+Y)) gives: cos ( y ) cos ( x ) ­ sin ( y ) sin ( x ) Example Typing: TEXPAND(COS(3·X)) gives: 4 cos ( x ) ­ 3 cos ( x ) 3 UNASSIGN Clear a variable UNASSIGN is used to clear a variable, for example: UNASSIGN(ABC) Computer Algebra System (CAS) 14-15 hp40g+. book Page 16 Friday, December 9, 2005 1:03 AM DIFF menu DERIV Derivative and partial derivative DERIV has two arguments: an expression (or a function) and a variable. DERIV returns the derivative of the expression (or the function) with respect to the variable given as the second parameter (used for calculating partial derivatives). Example Calculate: ) (x y z + x y--------------------------------------------z Typing: DERIV(X·Y2·Z3 + X·Y, Z) gives: 3xy z 2 2 2 3 DERVX Derivative DERVX has one argument: an expression. DERVX calculates the derivative of the expression with respect to the variable stored in VX. For example, given: x x+1 f ( x ) = ------------- + ln ----------- 2 x ­ 1 x ­1 calculate the derivative of f. Type: XX+1 DERVX -------------- + LN ------------ X ­ 1 2 X ­1 Or, if you have stored the definition of f(x) in F, that is, if you have typed: XX+1 TORE -------------- + LN ------------ , F 2 X ­ 1 X ­1 then type: 14-16 Computer Algebra System (CAS) hp40g+. book Page 17 Friday, December 9, 2005 1:03 AM DERVX(F) Or, if you have defined F(X) using DEF, that is, if you have typed: X X+1 DEF(F(X) = -------------- + LN ------------ 2 X ­ 1 X ­1 then type: DERVX(F(X)) Simplify the result to get: 3x ­1 ­ -------------------------------4 2 x ­2x +1 2 DIVPC Division in increasing order by exponent DIVPC has three arguments: two polynomials A(X) and B(X) (where B(0) 0), and a whole number n. [. . . ] However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: · · · · Reorient or relocate the receiving antenna. Increase the separation between the equipment and the receiver. Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. [. . . ]