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Limit Computation
The following problem reviews some important skills from precalculus. So, let’s take a look:
Computation of this limit starts with analysis of a rational function, then uses the graph of the natural logarithmic function.
First, by Laws of Logarithms, we obtain
Now, as x approaches ∞, we will first investigate where the blue goes.
Each of the three small fractions 3/x, 1/x2, and another 1/x2 will approach 0. And, since x approaches +∞, we also see that each of these small fractions remains positive. Symbolically, we could describe this analysis as:
From the graph of v = ln(u) below, we know that v now approaches –∞. This is the answer.
As we see in the graph, as the input approaches 0+, the output of the ln function approaches –∞.
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Disclaimer • Updated September 4, 2008
Email: mitsuma@kutztown.edu
Phone: +1 (610) 462-WPJW
Phone: +1 (610) 462-WPJW