User manual CASIO FX-570ES

[. . . ] E fx-570ES User's Guide http://world. casio. com/edu/ RCA502107-001V01 CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany About this Manual · The MATH mark indicates an example that uses Math format, while the LINE mark indicates Linear format. For details about input/output formats, see "Specifying the Input/Output Format". · Keycap markings indicate what a key inputs or what function it performs. · Pressing the 1 or S key followed by a second key performs the alternate function of the second key. [. . . ] · When performing an integration calculation involving trigonometric functions, specify Rad as the calculator's default angle unit. · Integration calculations can take considerable time to complete. · A smaller tol value provides better precision, but it also causes the calculation to take more time. · There may be large error in obtained integration values and errors may occur due to the type of function being integrated, the presence of positive and negative values in the integration interval, or the interval. · Pressing A will interrupt an ongoing integration calculation. E-34 Tips on Improving Integration Value Accuracy · When a periodic function or integration interval results in positive and negative f(x) function values Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results. S Positive S Negative b a f(x)dx = c a f(x)dx + (­ b c f(x)dx) Positive Part (S Positive) Negative Part (S Negative) · When integration values fluctuate widely due to minute shifts in the integration interval Divide the integration interval into multiple parts (in a way that breaks areas of wide fluctuation into small parts), perform integration on each part, and then combine the results. b a f(x)dx = x1 a f(x)dx + x2 x1 f(x)dx + . . . . . + b x4 f(x)dx Appendix <#031> (ln(x), 1, e) = 1 1 ­7 = 0. 8 <#032> 2 , 1, 5, 1×10 (tol specification omitted. ) (x ) E-35 k Differential Calculations Your calculator performs differential calculations by approximating the derivative based on centered difference approximation. d/dx( f(x), a, tol ) f(x): Function of X (All non-X variables are treated as constants. ) a: Input a value to specify the point for which the derivative should be obtained (differential point) tol: Tolerance range (input/output format: Linear) · You can omit specification of the tolerance range. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, or tol. · Differential calculations can be performed in the COMP Mode only. · When performing a differential calculation involving trigonometric functions, specify Rad as the calculator's default angle unit. · A "Time Out" error occurs when a differential calculation ends without the ending condition being fulfilled. · A smaller tol value provides better precision, but it also causes the calculation to take more time. · Inaccurate results and errors can be caused by the following : - discontinuous points in x values - extreme changes in x values - inclusion of the local maximum point and local minimum point in x values - inclusion of the inflection point in x values - inclusion of undifferentiable points in x values - differential calculation results approaching zero · Pressing A will interrupt an ongoing differential calculation. Appendix <#033> Determine f '( ) when f(x) = sin(x) 2 (tol specification omitted. ) <#034> d (3x2 ­ 5x + 2, 2, 1×10­12) = 7 dx E-36 With (, you can obtain the sum of an input f(x) expression for a specific range. calculations are performed using the following formula. k Calculations ( f(x), a, b) = f(a) + f(a + 1) + . . . . + f(b) f(x): Function of X (All non-X variables are treated as a: b: constants. ) Calculation range start point Calculation range end point · a and b are integers in the range of ­1 × 10 10 < a < b < 1 × 1010. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, or b. Appendix <#035> (X + 1, 1, 5) = 20 k Rectangular-Polar Coordinate Conversion Rectangular Coordinates (Rec) Polar Coordinates (Pol) · Coordinate conversion can be performed in the COMP, STAT, MATRIX, and VECTOR calculation modes. Converting to Polar Coordinates (Pol) Pol(X, Y) X: Specifies the rectangular coordinate X value Y: Specifies the rectangular coordinate Y value · Calculation result is displayed in the range of ­180° < < 180°. · Calculation result is displayed using the calculator's default angle unit. · Calculation result r is assigned to variable X, while is assigned to Y. Converting to Rectangular Coordinates (Rec) Rec(r, ) r : Specifies r value of polar coordinate : Specifies value of polar coordinate · Input value is treated as an angle value, in accordance with the calculator's default angle unit setting. · Calculation result x is assigned to variable X, while y is assigned to Y. E-37 · If you perform coordinate conversion inside of an expression instead of a stand-alone operation, the calculation is performed using only the first value (either the r-value or the X-value) produced by the conversion. [. . . ] · Action · Make necessary corrections. Argument ERROR · Cause · There is a problem with the argument of the calculation you are performing. E-69 · Action · Make necessary corrections. Dimension ERROR (MATRIX and VECTOR Modes only) · Cause · The matrix or vector you are trying to use in a calculation was input without specifying its dimension. · You are trying to perform a calculation with matrices or vectors whose dimensions do not allow that type of calculation. · Action · Specify the dimension of the matrix or vector and then perform the calculation again. · Check the dimensions specified for the matrices or vectors to see if they are compatible with the calculation. Variable ERROR (SOLVE feature only) · Cause · You did not specify a solution variable, and there is no X variable in the equation you input. [. . . ]