Question

determine the end - behavior of the following transcendental function by evaluating appropriate limits. then provide a simple sketch of the associated graph, showing asymptotes if they exist. f(x)=1 - ln x
determine the end - behavior of the given function. select the correct below and, if necessary, fill in the answer boxes to complete your choice.
a. neither lim(x→∞)(1 - ln x) nor lim(x→0⁺)(1 - ln x) exists and neither is ∞ nor -∞
b. lim(x→∞)(1 - ln x)= and lim(x→0⁺)(1 - ln x)=
question 2.5.14 1/1 pt
question 2.5.15 1/1 pt
question 2.5.57 1/1 pt

Explanation:

Step1: Analyze limit as $x\to\infty$

As $x\to\infty$, the natural - logarithm function $\ln x\to\infty$. So, $\lim_{x\to\infty}(1 - \ln x)=1-\infty=-\infty$.

Step2: Analyze limit as $x\to0^{+}$

As $x\to0^{+}$, the natural - logarithm function $\ln x\to-\infty$. So, $\lim_{x\to0^{+}}(1 - \ln x)=1-(-\infty)=\infty$.

Answer:

B. $\lim_{x\to\infty}(1 - \ln x)=-\infty$ and $\lim_{x\to0^{+}}(1 - \ln x)=\infty$