Texas Instruments Titanium TI-89, User Manual

Page: 812 / 977

Appendix A: Functions and Instructions 809
left()
MATH/String menu
left( sourceString [ , num ] )
⇒
string
Returns the leftmost
num
characters contained in
character string
sourceString
.
If you omit
num
, returns all of
sourceString
.
left("Hello",2)
¸
"He"
left(
list1
[ ,
num
] )
⇒
list
Returns the leftmost
num
elements contained in
list1
.
If you omit
num
, returns all of
list1
.
left({1,3,
ë
2,4},3)
¸
{1 3
ë
2}
left( comparison )
⇒
expression
Returns the left-hand side of an equation or
inequality.
left(x<3)
¸
x
limit()
MATH/Calculus menu
limit(
expression1
,
var
,
point
[ ,
direction
] )
⇒
expression
limit(
list1
,
var
,
point
[ ,
direction
] )
⇒
list
limit(
matrix1
,
var
,
point
[ ,
direction
] )
⇒
matrix
Returns the limit requested.
direction: negative=from left, positive=from right,
otherwise=both. (If omitted,
direction
defaults to
both.)
limit(2x+3,x,5)
¸
13
limit(1/x,x,0,1) ¸ ˆ
limit(sin(x)/x,x,0)
¸
1
limit((sin(x+h)
-
sin(x))/h,h,0)
¸
cos(x)
limit((1+1/n)^n,n,
ˆ
)
¸ e
Limits at positive
ˆ
and at negative
ˆ
are always
converted to one-sided limits from the finite side.
Depending on the circumstances,
limit()
returns
itself or
undef
when it cannot determine a unique
limit. This does not necessarily mean that a unique
limit does not exist.
undef
means that the result is
either an unknown number with finite or infinite
magnitude, or it is the entire set of such numbers.
limit()
uses methods such as L’Hopital’s rule, so
there are unique limits that it cannot determine. If
expression1
contains undefined variables other than
var
, you might have to constrain them to obtain a
more concise result.
Limits can be very sensitive to rounding error. When
possible, avoid the
APPROX
setting of the
Exact/Approx
mode and approximate numbers
when computing limits. Otherwise, limits that should
be zero or have infinite magnitude probably will not,
and limits that should have finite non-zero
magnitude might not.
limit(a^x,x, ˆ ) ¸ undef
limit(a^x,x,
ˆ
)|a>1
¸ ˆ
limit(a^x,x,
ˆ
)|a>0 and a<1
¸
0