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RPN Power 48 manual · Chapter 14 of 19

Algebra and calculus

Expressions on the stack, derivatives, integrals, solving equations, expanding, factoring and substituting.

14.1Type an algebraic expression#

An expression goes between single quotes. Inside the quotes the keys type their text: + types a plus, yˣ a power sign, and parentheses come from right shift 8. Names that hold no value stay as symbols.

Example 14.1

Type x squared

  1. Quote, x, power, 2, ENTER.

    'αα◀1/x÷αTyˣ2ENTER
Result of the example "Type x squared" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 'x^2'.
You should see'x^2'
Example 14.2

Evaluate with a value

  1. Store 3 in x, then evaluate x squared plus 1.

    3'αα◀1/x÷αENTERSTO▶'αα◀1/x÷αTyˣ2+1ENTEREVAL
Result of the example "Evaluate with a value" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 10 / x .
You should see1: 10

14.2The SYMB menu#

SYMB page 1: derivative, integral, SOLVE, ISOL, ZEROS, TAYLR. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / ∂ ∫ SOLVE ISOL ZEROS TAYLR.
SYMB page 1: derivative, integral, SOLVE, ISOL, ZEROS, TAYLR.
SYMB page 2: EXPAND, FACTOR, COLLECT, SIMPLIFY, SUBST, →NUM. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / EXPAN FACTOCOLLE SIMPLSUBST →NUM .
SYMB page 2: EXPAND, FACTOR, COLLECT, SIMPLIFY, SUBST, →NUM.

14.3Take a derivative#

Put the expression on level 2 and the variable name on level 1, then press the derivative key (right shift EVAL, or the first key of SYMB).

ddxx3=3x2\frac{d}{dx}x^{3}=3x^{2}
Example 14.3

Derivative of x cubed

  1. Type the expression and the name x, then press the derivative key.

    'αα◀1/x÷αTyˣ3ENTER'αα◀1/x÷αENTER▶∂EVAL
Result of the example "Derivative of x cubed" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: '3*x^2'.
You should see'3*x^2'
Example 14.4

Derivative of x squared

  1. The same with the SYMB menu key.

    'αα◀1/x÷αTyˣ2ENTER'αα◀1/x÷αENTER◀SYMB'F1
Result of the example "Derivative of x squared" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: '2*x' / ∂ ∫ SOLVE ISOL ZEROS TAYLR.
You should see'2*x'

See also Differentiate with a formula answer

14.4Integrate between two limits#

The integral key (right shift quote) needs four objects: the lower limit, the upper limit, the expression and the variable name, in that order from level 4 to level 1.

∫03x2 dx=9\int_{0}^{3}x^{2}\,dx=9
Example 14.5

Integral of x squared from 0 to 3

  1. Push 0, 3, the expression and the name x, then press right shift quote.

    0ENTER3ENTER'αα◀1/x÷αTyˣ2ENTER'αα◀1/x÷αENTER▶∫'
Result of the example "Integral of x squared from 0 to 3" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 9.
You should see1: 9

See also Integrate with a formula answer

14.5Solve an equation#

SOLVE takes an equation (use left shift + for the equals sign) and the unknown name, and returns the list of solutions. ISOL returns one solution. ZEROS returns the numbers that make an expression zero.

x2−4=0  ⇒  x=±2x^{2}-4=0\;\Rightarrow\;x=\pm2
Example 14.6

Solve x squared minus 4 equals 0

  1. Type the equation, using left shift +/− for the equals sign, then the name, then SOLVE (SYMB, third key).

    'αα◀1/x÷αTyˣ2−4◀=+/−0ENTER'αα◀1/x÷αENTER◀SYMB'F3
Result of the example "Solve x squared minus 4 equals 0" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: { 'x=-2' 'x=2' } / ∂ ∫ SOLVE ISOL ZEROS TAYLR.
You should see{ 'x=-2' 'x=2' }
Example 14.7

Zeros of an expression

  1. ZEROS is the fifth key.

    'αα◀1/x÷αTyˣ2−4ENTER'αα◀1/x÷αENTER◀SYMB'F5
Result of the example "Zeros of an expression" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: { -2 2 } / ∂ ∫ SOLVE ISOL ZEROS TAYLR.
You should see{ -2 2 }

See also Solve an equation exactly

14.6Expand, factor and simplify#

Example 14.8

Expand (x+1) squared

  1. Type the expression with parentheses (right shift 8) and press EXPAND (SYMB page 2, first key).

    '▶( )8αα◀1/x÷α+1▶yˣ2ENTER◀SYMB'NXTF1
Result of the example "Expand (x+1) squared" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 'x^2+2*x+1' / EXPAN FACTOCOLLE SIMPLSUBST →NUM .
You should see'x^2+2*x+1'
Example 14.9

Factor x squared minus 1

  1. FACTOR is the second key.

    'αα◀1/x÷αTyˣ2−1ENTER◀SYMB'NXTF2
Result of the example "Factor x squared minus 1" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: '(x-1)*(x+1)' / EXPAN FACTOCOLLE SIMPLSUBST →NUM .
You should see'(x-1)*(x+1)'

14.7Substitute a value#

Example 14.10

Substitute x = 3 into x squared

  1. Type the expression and the equation x=3, then SUBST (SYMB page 2, fifth key).

    'αα◀1/x÷αTyˣ2ENTER'αα◀1/x÷α◀+/−3ENTER◀SYMB'NXTF5
Result of the example "Substitute x = 3 into x squared" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 9 / EXPAN FACTOCOLLE SIMPLSUBST →NUM .
You should see1: 9

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