Maple Tutor

Part 12: Limits

1. Limits are easy to calculate in Maple. As a test we'll calculate the limit of sin(x)/x as x approaches 0. If necessary, unassign x:
   x:='x'
   Then enter
   sin(x)/x
   Use your mouse to highlight this expression, click the right mouse button, and select "Limit".  In the pop-up window which appears, enter "0" for the limit point and click "OK". Maple should make an arrow pointing to the desired output. (In Maple versions 11 and higher the arrow has a label.)
   

2. The Maple limit command also calculates limits at infinity. Calculate the limit of
   (1 + x³)/((1 + x)(1+2x²))
   as x approaches infinity using the same method. (Make sure you have a multiplication symbol in the denominator.) Type the word "infinity" into the limit point box.

3. The standard limit command will deal with one-sided limits if there is no possibility of confusion. Calculate the limit of
   (√x)/(√(x + x²))
   as x approaches 0. Use the "Expression" palette to get the square root symbol.
   

   Now try to calculate
   |x|/x
   as x approaches 0.

   Why is this limit ambiguous? Try clicking the "from right" button in the pop-up window. Then try clicking the "from left" button.