User manual HP 50G GRAPHING CALCULATOR

[. . . ] HP g graphing calculator user's guide H Edition 1 HP part number F2229AA-90006 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. 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 16399 West Bernardo Drive MS 8-600 San Diego, CA 92127-1899 USA Printing History Edition 1 April 2006 Preface You have in your hands a compact symbolic and numerical computer that will facilitate calculation and mathematical analysis of problems in a variety of disciplines, from elementary mathematics to advanced engineering and science subjects. [. . . ] In these cases, the equation was re-written with all its terms moved to the left-hand side of the equal sign. Also, the equal sign was removed, but it is understood that the resulting expression is equal to zero. Implicit derivatives Implicit derivatives are possible in expressions such as: Application of derivatives Derivatives can be used for analyzing the graphs of functions and for optimizing functions of one variable (i. e. , finding maxima and minima). Some applications of derivatives are shown next. Page 13-7 Analyzing graphics of functions In Chapter 11 we presented some functions that are available in the graphics screen for analyzing graphics of functions of the form y = f(x). These functions include (X, Y) and TRACE for determining points on the graph, as well as functions in the ZOOM and FCN menu. The functions in the ZOOM menu allow the user to zoom in into a graph to analyze it in more detail. Within the functions of the FCN menu, we can use the functions SLOPE, EXTR, F', and TANL to determine the slope of a tangent to the graph, the extrema (minima and maxima) of the function, to plot the derivative, and to find the equation of the tangent line. Press , , , simultaneously in RPN mode, to access to the PLOT SETUP window. Press , , , simultaneously, to access the PLOT window Change H-VIEW range to 2 to 2, and V-VIEW range to 5 to 5. The resulting plot looks as follows: Notice that there are vertical lines that represent asymptotes. These are not part of the graph, but show points where TAN(X) goes to at certain values of X. Press @TRACE @(X, Y)@, and move the cursor to the point X: 1. 08E0, Y: 1. 86E0. This operation produces the equation of the tangent line, and plots its graph in the same figure. The result is shown in the figure below: Page 13-8 Press L @PICT @CANCL $ to return to normal calculator display. Notice that the slope and tangent line that you requested are listed in the stack. Function DOMAIN Function DOMAIN, available through the command catalog (, N), provides the domain of definition of a function as a list of numbers and specifications. For example, indicates that between and 0, the function LN(X) is not defined (?), while from 0 to +, the function is defined (+). On the other hand, indicates that the function is not defined between and -1, nor between 1 and +. The domain of this function is, therefore, -1<X<1. Function TABVAL This function is accessed through the command catalog or through the GRAPH sub-menu in the CALC menu. Function TABVAL takes as arguments a function of the CAS variable, f(X), and a list of two numbers representing a domain of interest for the function f(X). Function TABVAL returns the input values plus the range of the function corresponding to the domain used as input. For example, Page 13-9 This result indicates that the range of the function f (X ) = 1 X 2 +1 corresponding to the domain D = { -1, 5 } is R = 2 26 , . 2 26 Function SIGNTAB Function SIGNTAB, available through the command catalog (, N), provides information on the sign of a function through its domain. For example, for the TAN(X) function, SIGNTAB indicates that TAN(X) is negative between /2 and 0, and positive between 0 and /2. 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Service Europe Country : Austria Belgium Denmark Eastern Europe countries Finland France Germany Greece Holland Italy Norway Portugal Spain Sweden Telephone numbers +43-1-3602771203 +32-2-7126219 +45-8-2332844 +420-5-41422523 +358-9-640009 +33-1-49939006 +49-69-95307103 +420-5-41422523 +31-2-06545301 +39-02-75419782 +47-63849309 +351-229570200 +34-915-642095 +46-851992065 Page LW-2 Switzerland Turkey UK Czech Republic South Africa Luxembourg Other European countries Asia Pacific Country : Australia Singapore L. America Country : Argentina Brazil Mexico Venezuela Chile Columbia Peru Central America & Caribbean Guatemala Puerto Rico Costa Rica N. America Country : U. S. +41-1-4395358 (German) +41-22-8278780 (French) +39-02-75419782 (Italian) +420-5-41422523 +44-207-4580161 +420-5-41422523 +27-11-2376200 +32-2-7126219 +420-5-41422523 Telephone numbers +61-3-9841-5211 +61-3-9841-5211 Telephone numbers 0-810-555-5520 Sao Paulo 3747-7799; ROTC 0800-157751 Mx City 5258-9922; ROTC 01800-472-6684 0800-4746-8368 800-360999 9-800-114726 0-800-10111 1-800-711-2884 1-800-999-5105 1-877-232-0589 0-800-011-0524 Telephone numbers 1800-HP INVENT (905) 206-4663 or 800- HP Canada INVENT ROTC = Rest of the country Please logon to http://www. hp. com for the latest service and support information. Page LW-3 Regulatory information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. [. . . ]