Michael J. answered • 11/28/15
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Mastery of Limits, Derivatives, and Integration Techniques
When x approaches a certain value from either direction, the function gets closer to a certain constant. There are two ways to do this.
1) Plug in x=1 into the limit and use L'Hospital Rule (derivative of numerator divided by derivative of denominator) when needed. Only use the rule when the limit is indeterminate such as 0/0 and ∞/∞.
2) Analyze the characteristics of the function.
We use method 2.
Notice that if we plug in x=1 into the limit, the limit is undefined. This is because (1 - 1)2 is zero. x=1 is a vertical asymptote. Because x=1 is a vertical asymptote, f(x) increases infinitely as it approaches x=1.
