Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).

 

Incremental power mode must be set (flag –114 set).

Example:

Find the fourth degree Taylor polynomial for the following:

 

x3 + 4x + 12

 

 

-----------------------------

 

 

11x11 + 1

 

Command:

DIVPC(X^3+4*X+12,11*X^11+1,4)

Result:

12+4*X+X^3

 

See also:

TAYLOR0, TAYLR, SERIES

 

 

 

dn

 

 

Type:

Function

 

Description:

Differential of a function with respect to its argument n. For example d1f(x,y) is the differential of

 

f(x,y) with respect to x and d3g(y,z,t) is the differential of g(y,z,t) with respect to t. The second-

 

order derivative of f(x,y) with respect to x is written d1d1f(x,y). The dn function is an alternative

 

to the ∂ function; d1f(x,y) is the same as ∂x(f(x,y)). dn does not require brackets after it, it must be

 

followed immediately by the function name, with no spaces. dn differentiates with respect to the

 

whole of argument n, see the example. dn is mainly used for formal arguments, see the example in

 

DESOLVE, but can be used to differentiate expressions, as in the example.

Access:

Access is by typing the letter “d” from the alpha keyboard, followed by the number n, before the

 

function whose differential is required.

Output:

dn does not change its argument, it works like the negative sign placed before a number or an

 

expression. If the argument can be differentiated, Nwill carry out the differentiation.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

 

Radians mode must be set (flag –17 set).

Example:

Differentiate the function sin(2x) with respect to its argument:

Command:

EVAL(d1SIN(2*X))

 

Result:

COS(2*X)

 

 

(Note that the function was differentiated with respect to its argument 2x, not with respect to the

 

variable x.)

 

See also:

DERIV, DERVX, DESOLVE, ∂

 

 

 

DO

Command

 

Type:

 

Description:

DO Indefinite Loop Structure Command: Starts DO…UNTIL…END indefinite loop structure.

 

DO … UNTIL … END executes a loop repeatedly until a test returns a true (nonzero) result.

 

Since the test clause is executed after the loop clause, the loop is always executed at least once.

 

The syntax is: DO loop-clause

UNTIL test-clause END

 

DO starts execution of the loop clause. UNTIL ends the loop clause and begins the test clause.

 

The test clause must return a test result to the stack. END removes the test result from the stack.

 

If its value is zero, the loop clause is executed again; otherwise execution resumes following

 

END.

 

Access:

!°BRANCH DO

( °is the left-shift of the Nkey).

3-64 Full Command and Function Reference