Il logo di batmath
previous page | next page

Examples and further techniques

Through the examples in this page we show some of the most common techniques used in the calculation of limits.

  1. img . Use this technique when searching the limit of a rational function with x→±∞.

  2. img.

  3. img. Change the variable from x to t=1/x. As x tends to zero, t tends to infinity. Thus  img.

  4. img

  5. img. Change the variable from x to ex-1=t. As x tends to zero, t tends also to zero. The limit transforms in the reciprocal of limit 4: img.

  6. img. This technique often works in the case of a rational function in the form 0/0.

  7. img.

  8. img.

  9. img. Here we have implicitly used a substitution x2=t. As x tends to zero, also t tends to zero. We can treat many other cases in the same way: usually the substitution will not be written explicitly. See the following example.

  10. img.

previous page | next page
first published on march 26 2002 - last updated on september 01 2003