Subjects calculus

Limit Logarithmic 689Ff6

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1. The problem asks to write a limit that represents the behavior of the function $a(x) = -1.12 \log_6 x$ as $x$ approaches 0 from the right. 2. Recall the properties of logarithmic functions: for $\log_b x$ with base $b>1$, as $x \to 0^+$, $\log_b x \to -\infty$. 3. Since $a(x) = -1.12 \log_6 x$, multiplying by $-1.12$ reverses the sign of the logarithm's output. 4. Therefore, as $x \to 0^+$, $\log_6 x \to -\infty$, so $$a(x) = -1.12 \log_6 x \to -1.12 \times (-\infty) = +\infty.$$ 5. The limit expression is: $$\lim_{x \to 0^+} -1.12 \log_6 x = +\infty.$$ This means the function grows without bound positively as $x$ approaches 0 from the right.