Through the examples in this page we show some of the most common techniques used in the calculation of limits.
. Use this technique when searching the limit of a rational function with x→±∞.
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. Change the variable from x to t=1/x. As x tends to zero, t tends to infinity. Thus .
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. Change the variable from x to e^{x}-1=t. As x tends to zero, t tends also to zero. The limit transforms in the reciprocal of limit 4: .
. This technique often works in the case of a rational function in the form 0/0.
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. Here we have implicitly used a substitution x^{2}=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.
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