let k be the logarithmic function given by k(x)=1/4 log10 x. which of the following limit statements about…

let k be the logarithmic function given by k(x)=1/4 log10 x. which of the following limit statements about the graph of k is true? lim x→∞ k(x)=∞ lim x→0+ k(x)=∞ lim x→∞ k(x)=−∞ lim x→∞ k(x)=0

let k be the logarithmic function given by k(x)=1/4 log10 x. which of the following limit statements about the graph of k is true? lim x→∞ k(x)=∞ lim x→0+ k(x)=∞ lim x→∞ k(x)=−∞ lim x→∞ k(x)=0

Answer

Explanation:

Step1: Recall logarithm properties

The function is $k(x)=\frac{1}{4}\log_{10}x$. The domain of $y = \log_{10}x$ is $x>0$.

Step2: Analyze limit as $x\to\infty$

As $x$ approaches infinity, the logarithm function $\log_{10}x$ grows without bound. Since $k(x)=\frac{1}{4}\log_{10}x$, we have $\lim_{x\to\infty}k(x)=\lim_{x\to\infty}\frac{1}{4}\log_{10}x=\infty$.

Step3: Analyze limit as $x\to0^{+}$

As $x$ approaches $0$ from the right, $\log_{10}x$ approaches $-\infty$. So $\lim_{x\to0^{+}}k(x)=\lim_{x\to0^{+}}\frac{1}{4}\log_{10}x = -\infty$.

Answer:

$\lim_{x\to\infty}k(x)=\infty$