[. . . ] E fx-570ES PLUS fx-991ES PLUS User's Guide CASIO Worldwide Education Website http://edu. casio. com CASIO EDUCATIONAL FORUM http://edu. casio. com/forum/ Contents Important Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Sample Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Initializing the Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Safety Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [. . . ] Precautions for Integration Calculation Only · Integration normally requires considerable time to perform. 1 · For f(x) 0 where a x b (as in the case of 0 3x2 ­ 2 = ­1), calculation will produce a negative result. · Depending on the content of f(x) and the region of integration, calculation error that exceeds the tolerance may be generated, causing the calculator to display an error message. Precautions for Differential Calculation Only · If convergence to a solution cannont be found when tol input is omitted, the tol value will be adjusted automatically to determine the solution. · Non-consecutive points, abrupt fluctuation, extremely large or small points, inflection points, and the inclusion of points that cannot be differentiated, or a differential point or differential calculation result that approaches zero can cause poor precision or error. E-15 Tips for Successful Integration Calculations 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. b a c b f(x)dx = a f(x)dx + (­ c f(x)dx) S Positive S Negative Positive Part Negative Part (S Positive) (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. f (x) b a x x1 x2 f(x)dx = b a f(x)dx + x1 f(x)dx + . . . . . + 0 a x1 x2 x3 x4 b x4 f(x)dx Examples 1 sin 30°= 0. 5 sin-10. 5 = 30° 2 sinh 1 = 1. 175201194 cosh­1 1 = 0 3 /2 radians = 90°, 50 grads = 45° () 2 50 4 To calculate e5 (SETUP) (DRG ) (DRG ) (r) (g) 30 (sin-1) 0. 5 (sinh) 1 (cosh-1) 1 0. 5 30 1. 175201194 0 90 45 2 to three significant digits (Sci 3) ( )5 ( )5 2 2 1000 2 (, ) 16 2 16 (Sci) 2. 97×102 2. 97×102 3 4 4 4. 50×100 5 log101000 = log 1000 = 3 log216 = 4 6 To calculate ln 90 (= loge 90) to three significant digits (Sci 3) (SETUP) 7 1. 2 (Sci) 1. 2 1 5 5 1 ( ( 90 10 2 )5 ) 32 3 2 (x3) 32 103 = 1200 (1+1)2+2 = 16 (52)3 = 15625 5 32 = 2 1200 16 15625 2 2 E-16 To calculate ' × 3 (= 3' = 4. 242640687. . . ) to three decimal 2 2 places (Fix 3) (SETUP) (Fix) 2 3 3' 2 2 8 1ln(x) e 3 4. 243 4. 243 =1 (X) 1 1 (X) (, ) (e) (e) (, ) 1 1 9 To obtain the derivative at point x = /2 for the function y = sin(x) ( ( (, ) 5 ) () ) () 2 (X) 2 (X) 0 0 10 x =1 (x + 1) = 20 ( ( ) ) (X) 1 1 (X) 1 (, ) 5 5 (, ) 1 20 20 11 To convert rectangular coordinates (' , ' ) to polar coordinates 22 (Pol) (Pol) 2 2 (, ) (, ) 2 2 r=2, =45 r= 2 = 45 To convert polar coordinates (' , 45°) to rectangular coordinates 2 (Rec) 12 (5 + 3) != 40320 13 2 ­ 7 2 = 10 (Abs) 2 (Abs) 2 7 7 2 2 2 5 3 (, ) 45 (x!) X=1, Y=1 40320 10 10 459 48 117 14 To obtain three random three-digit integers 1000 (Ran#) (Results shown here are for illustrative purposes only. Actual results will differ. ) E-17 15 To generate random integers in the range of 1 to 6 (RanInt) 1 (, ) 6 2 6 1 (Results shown here are for illustrative purposes only. Actual results will differ. ) 16 To determine the number of permutations and combinations possible when selecting four people from a group of 10 Permutations: Combinations: 10 10 (nPr) 4 (nCr) 4 5040 210 17 To perform the following calculations when Fix 3 is selected for the number of display digits: 10 ÷ 3 3 and Rnd(10 ÷ 3) 3 (SETUP) (Fix) (Rnd) 10 10 3 3 3 3 10. 000 9. 999 Complex Number Calculations (CMPLX) To perform complex number calculations, first press (CMPLX) to enter the CMPLX Mode. You can use either rectangular coordinates (a+bi) or polar coordinates (r ) to input complex numbers. Complex number calculation results are displayed in accordance with the complex number format setting on the setup menu. (2 + 6i) ÷ (2i) = 3 ­ i (Complex number format: a + bi) 2 6 (i) 2 (i) 2 45 = ' + ' i 2 2 3­i (Complex number format: a + bi) 2 ( ) 45 '+'i 22 (Complex number format: r ) 2 45 2 (i) ' + 'i = 2 2 2 45 2 Note: · If you are planning to perform input and display of the calculation result in polar coordinate format, specify the angle unit before starting the calculation. · The value of the calculation result is displayed in the range of ­180° 180°. · Display of the calculation result while Linear Display is selected will show a and bi (or r and ) on separate lines. CMPLX Mode Calculation Examples (1 ­ i)­1 = 1 + 1 i 22 (1 + i)2 + (1 ­ i)2 = 0 1 (i) (Complex number format: a + bi) 1 (i) 1+1i 22 0 1 (i) E-18 To obtain the conjugate complex number of 2 + 3i (Complex number format: a + bi) (CMPLX) (Conjg) 2 3 (i) To obtain the absolute value and argument of 1 + i Absolute Value: (Abs) 1 (i) Argument: (CMPLX) (arg)1 (i) 2­3i ' 2 45 Using a Command to Specify the Calculation Result Format Either of two special commands ( r or a+bi) can be input at the end of a calculation to specify the display format of the calculation results. The command overrides the calculator's complex number format setting. ' + ' i = 2 45, 2 2 2 2 (i) 2 ( ) 45 45 = ' + ' i 2 2 (CMPLX) ( r ) (CMPLX) ( a+bi) 2 2 45 '+'i 22 Using CALC CALC lets you save calculation expressions that contain variables, which you can then recall and execute in the COMP Mode ( ) and the CMPLX Mode ( ). The following describes the types of expressions you can save with CALC. · Expressions: 2X + 3Y, 2AX + 3BY + C, A + Bi · Multi-statements: X + Y : X (X + Y) · Equalities with a single variable on the left and an expression including variables on the right: A = B + C, Y = X2 + X + 3 (=) to input the equals sign of the equality. ) (Use To store 3A + B and then substitute the following values to perform the calculation: (A, B) = (5, 10), (7, 20) 3 (A) (B) Math Prompts for input of a value for A Current value of A 5 10 (or ) E-19 7 20 To exit CALC: To store A + Bi and then determine ' + i, 1 + ' i using polar 3 3 coordinates (r ) (CMPLX) (B) (i) ( r ) 1 3 CMPLX Math (A) (CMPLX) 3 (or )1 To exit CALC: Note: During the time from when you press until you exit CALC by pressing , you should use Linear Display input procedures for input. Using SOLVE SOLVE uses Newton's Law to approximate the solution of equations. The following describes the types of equations whose solutions can be obtained using SOLVE. · Equations that include variable X: X2 + 2X ­ 2, Y = X + 5, X = sin(M), X +3=B+C SOLVE solves for X. · Equations input using the following syntax: {equation}, {solution variable} SOLVE solves for Y, for example, when an equation is input as: Y = X + 5, Y Important: · If an equation contains input functions that include an open parenthesis (such as sin and log), do not omit the closing parenthesis. · The following functions are not allowed inside of an equation: , d/dx, , Pol, Rec. To solve y = ax2 + b for x when y = 0, a = 1, and b = ­2 (Y) (X) (=) (A) (B) Math (SOLVE) Prompts for input of a value for Y Current value of Y E-20 Math 0 1 2 Current value of X Input an initial value for X (Here, input 1): 1 Solution screen To exit SOLVE: Note: During the time from when you press (SOLVE) until you exit SOLVE by pressing , you should use Linear Display input procedures for input. [. . . ] Check the calculation expression to make sure that it does not contain any errors. Make sure that you are using the correct mode for the type of calculation you are trying to perform. If the above steps do not correct your problem, press the cause the calculator to perform a routine that checks whether calculation functions are operating correctly. If the calculator discovers any abnormality, it automatically initializes the calculation mode and clears memory contents. E-41 For details about initialized settings, see 'Configuring the Calculator Setup'. [. . . ]