User manual CASIO FX-115D

[. . . ] 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 BASE-N Mode to access the function. · The following shows an example of how an alternate function operation is represented in this User's Guide. [. . . ] · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, b, or tol. · Integration calculations can be performed in the COMP Mode only. · The integration result will be negative when f(x) < 0 within an integration interval that conforms with a < x < b. Example: (0. 5X2 ­ 2, ­2, 2) = ­5. 333333333 · A "Time Out" error occurs when an integration calculation ends without the ending condition being fulfilled. · 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 <#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. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, or tol. 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. n (n is an integer. ) d a b (depending on fraction display format c or c setting) · Transformation to a fractional form is limited to inverse trigonometric function results and values that are normally expressed in radians. · After obtaining a calculation result in ' form, you can convert it to decimal form by pressing the f key. [. . . ] · 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. [. . . ]