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Final answer:
The left-hand limit of the function f(x) as x approaches 2 is 0.5, obtained by canceling out common factors and observing values slightly less than 2.
Explanation:
The student's question involves finding the left-hand limit of the function f(x) = (x² - 2x)/(x² - 4) as x approaches 2. To determine this limit, we look at values of x that are close to but less than 2. A direct substitution would lead to a division by zero, which is undefined. Therefore, we factor the expressions to simplify the function. Upon factoring x² - 4 as (x + 2)(x - 2), we can cancel out the (x - 2) term that occurs in both the numerator and the denominator, given that x is not exactly 2. Doing so, the simplified expression would be f(x) = x as x approaches 2 from the left. In this case, the table on p. 64 suggests that f(x) approaches 0.5 just before x reaches 2.
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Answer:
B. -∞
Step-by-step explanation:
There is a vertical asymptote at x=2. Left of that line, the denominator is negative. As x approaches 2 from the left, the function approaches negative infinity.
