(Course 2) Answer the following questions, where log is the natural logarithm. (1) Let $f ( x ) = x - 1 - \log x$. We are to find the minimum value of $f ( x )$. First, we have $$f ^ { \prime } ( x ) = \mathbf { A } - \frac { \mathbf { B } } { x } .$$ Examining the increases and decreases of the value of $f ( x )$, we see that at $x = \mathbf { C }$ the function is minimized and its value is $\mathbf { D }$. From this, we derive the inequality $x - 1 \geqq \log x$. (2) For $\mathbf { G }$ in the following sentences, choose the correct answer from among choices (0) $\sim$ (3) below. For the other $\square$, enter the correct number. Let $k$ be a positive real number and $n$ be a positive integer. We denote by $S$ the area of the figure bounded by the three straight lines $y = \frac { x } { n }$, $x = k$ and $y = 0$, and by $T$ the area of the figure bounded by the curve $y = \log x$, the straight line $x = k$ and the $x$ axis.
(Course 2) Answer the following questions, where log is the natural logarithm.\\
(1) Let $f ( x ) = x - 1 - \log x$. We are to find the minimum value of $f ( x )$.
First, we have
$$f ^ { \prime } ( x ) = \mathbf { A } - \frac { \mathbf { B } } { x } .$$
Examining the increases and decreases of the value of $f ( x )$, we see that at $x = \mathbf { C }$ the function is minimized and its value is $\mathbf { D }$. From this, we derive the inequality $x - 1 \geqq \log x$.\\
(2) For $\mathbf { G }$ in the following sentences, choose the correct answer from among choices (0) $\sim$ (3) below. For the other $\square$, enter the correct number.
Let $k$ be a positive real number and $n$ be a positive integer. We denote by $S$ the area of the figure bounded by the three straight lines $y = \frac { x } { n }$, $x = k$ and $y = 0$, and by $T$ the area of the figure bounded by the curve $y = \log x$, the straight line $x = k$ and the $x$ axis.