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The Maxima on-line user's manual

Algebra Calculator

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Limit

Function: limit (<expr>, <x>, <val>, <dir>)

f:sqrt(t^2+t+1)-t;
limit(f,t,inf);

Function: limit (<expr>, <x>, <val>)

Function: limit (<expr>) Computes the limit of <expr> as the real variable <x> approaches the value <val> from the direction <dir>. <dir> may have the value plus for a limit from above, minus for a limit from below, or may be omitted (implying a two-sided limit is to be computed).

limit uses the following special symbols: inf (positive infinity) and minf (negative infinity). On output it may also use und (undefined), ind (indefinite but bounded) and infinity (complex infinity).

infinity (complex infinity) is returned when the limit of the absolute value of the expression is positive infinity, but the limit of the expression itself is not positive infinity or negative infinity. This includes cases where the limit of the complex argument is a constant, as in limit(log(x), x, minf), cases where the complex argument oscillates, as in limit((-2)^x, x, inf), and cases where the complex argument is different for either side of a two-sided limit, as in limit(1/x, x, 0) and limit(log(x), x, 0).

lhospitallim is the maximum number of times LHospitals rule is used in limit. This prevents infinite looping in cases like limit (cot(x)/csc(x), x, 0).

tlimswitch when true will allow the limit command to use Taylor series expansion when necessary.

limsubst prevents limit from attempting substitutions on unknown forms. This is to avoid bugs like limit (f(n)/f(n+1), n, inf) giving 1. Setting limsubst to true will allow such substitutions.

limit with one argument is often called upon to simplify constant expressions, for example, limit (inf-1).

example (limit) displays some examples.

For the method see Wang, P., "Evaluation of Definite Integrals by Symbolic Manipulation", Ph.D. thesis, MAC TR-92, October 1971.

There are also some inexact matches for limit. Try ?? limit to see them.

(%o1)                                true
(%i2) 

Related Examples

limit

limit(((x+1)/(x-1)),x...

Calculate

limit

limit(((x^4-1)/(2*x^4...

limit(((x^3-2*x^2-4*x...

Calculate

limit-sqrt

limit((4-3*n)/(sqrt(1...

0;

Calculate

limit

limit((1-C)/((x-t)+3)...

Calculate

limit-log-plot2d
plot2d([f], [x,0,001,10]);

f: log (x) ;

limit (f, x, 0, plus);

limit (f, x, 0, minus);

Calculate

limit

f(t):=(((3*t^2+2)*(5*...

limit(f(t),t,7,plus);

Calculate

limit-minf-plot2d
plot2d(f(c),[c,-3,3]);

f(c):=c^2;

plot2d(f(c),[c,-3,3]);

limit(f(c),c,minf);

Calculate

limit

f(x):= 2 * x^2 + 3 * x;

g(x) = limit((f(x + ...

Calculate

limit

f(x)=2*x^2-4;

x0:3;

f(x0);

Calculate

limit

"*"/* Ableitung einer...

f(x):=x^2-8*x+15;

d:(f(x+h)-f(x))/h;

Calculate