User manual CASIO FX-971D

[. . . ] The alternate function is indicated by the text printed above the key. Alternate function sin {D} Keycap function ­1 s · The following shows what the different colors of the alternate function key text mean. If key marking text is this color: Yellow Red Purple (or enclosed in purple brackets) Green (or enclosed in green brackets) It means this: Press 1 and then the key to access the applicable function. Press S and then the key to input the applicable variable, constant, or symbol. Enter the CMPLX Mode to access the function. [. . . ] · You cannot input a tol value when using Math format. · 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 <#032> , 1, 5, 1×10­7 = 0. 8 2 (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. A default value of 1 × 10­10 is used when you do. · (, 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. Specify a tol value that is 1 × 10­14 or greater. Values actually generated by your calculator will be different. Permutation (nPr) and Combination (nCr) These functions make it possible to perform permutation and combination calculations. n and r must be integers in the range of 0 < r < n < 1 × 1010. Appendix <#041> How many four-person permutations and combinations are possible for a group of 10 people? E-38 Rounding Function (Rnd) This function rounds the value or the result of the expression in the function's argument to the number of significant digits specified by the number of display digits setting. Display Digits Setting: Norm1 or Norm2 The mantissa is rounded to 10 digits. Display Digits Setting: Fix or Sci The value is rounded to the specified number of digits. Example: 200 ÷ 7 × 14 = 400 LINE 200/7*14= (Specifies three decimal places. ) 1N6(Fix)3 FIX (Calculation is performed internally using 15 digits. ) FIX 200/7= FIX *14= The following performs the same calculation with rounding. FIX 200/7= (Round the value to the specified number of digits. ) FIX 10(Rnd)= E-39 (Check rounded result. ) FIX *14= k Practical Examples Appendix <#042> 0(sinX + cosX ) dX = 2 (tol: Not specified) <#043> Confirm that the two sides of the following equation are equal: e= 1 n=0 n! Transforming Displayed Values You can use the procedures in this section to transform a displayed value to engineering notation, or to transform between standard form and decimal form. k Using Engineering Notation A simple key operation transforms a displayed value to engineering notation. Appendix <#044> Transform the value 1, 234 to engineering notation, shifting the decimal point to the right. <#045> Transform the value 123 to engineering notation, shifting the decimal point to the left. k Using S-D Transformation You can use S-D transformation to transform a value between its decimal (D) form and its standard (S) form (fraction, ). Formats Supported for S-D Transformation S-D transformation can be used to transform a displayed decimal calculation result to one of the forms described below. Performing S-D transformation again converts back to the original decimal value. E-40 Note · When you transform from decimal form to standard form, the calculator automatically decides the standard form to use. Fraction: The current fraction display format setting determines whether the result is an improper fraction or mixed fraction. : The following are the forms that are supported. [. . . ] · Action · The equation you input must include an X variable when you do not specify the solution variable. · Specify a variable that is included in the equation you input as the solution variable. Can't Solve Error (SOLVE feature only) · Cause · The calculator could not obtain a solution. · Action · Check for errors in the equation that you input. · Input a value for the solution variable that is close to the expected solution and try again. Insufficient MEM Error · Cause · There is not enough memory to perform your calculation. [. . . ]