#### Examples.

- Input:
  limit(1/x,x,0,-1)
  or:
  limit(1/x,x=0,-1)
  Output:

  −∞

- Input:
  limit(1/x,x,0,1)
  or:
  limit(1/x,x=0,1)
  Output:

  +∞

- Input:
  limit(1/x,x,0,0)
  or:
  limit(1/x,x,0)
  or:
  limit(1/x,x=0)
  Output:

  ∞

  (Note that ∞ or infinity without an explicit + or - represents unsigned infinity.) Hence, abs(1/x) approaches +∞ when x approaches 0.

Exercises.

- Find, for n>2, the limit as x approaches 0 of:

  ntan(x)−tan(nx)
  sin(nx)−nsin(x)

  Input:
  limit((n*tan(x)-tan(n*x))/(sin(n*x)-n*sin(x)),x=0)
  Output:

  2

- Find the limit as x approaches +∞ of

  √

  x+

  √

  x+

  √

  x

  −

  √

  x

  Input:
  limit(sqrt(x+sqrt(x+sqrt(x)))-sqrt(x),x=+infinity)
  Output:

  1
  2

- Find the limit as x approaches 0 of

  √

  1+x+x2/2

  −exp(x/2)

  (1−cos(x))sin(x)

  Input:
  limit((sqrt(1+x+x^2/2)-exp(x/2))/((1-cos(x))*sin(x)),x,0)
  Output:

  −

  1
  6