Use inequalities to describe R in terms of its vertical and horizontal cross sections.R is the region bounded by y = e^x, y = 2, and x = 0 A) Vertical cross sections: $\begin{aligned} e ^ { x } & \leq x \leq 2 \ 0 & \leq y \leq \ln 2 \end{aligned}$ Horizontal cross sections: $\begin{array} { l } 0 \leq y \leq \ln 2 \ 1 \leq x \leq 2 \end{array}$ B) Vertical cross sections: $\begin{array} { c } e ^ { x } \leq x \leq \ln 2 \ 0 \leq y \leq 2 \end{array}$ Horizontal cross sections: $\begin{array} { l } 0 \leq y \leq 2 \ 1 \leq x \leq \ln 2 \end{array}$ C) Vertical cross sections: $\begin{aligned} 0 & \leq x \leq \ln y \ e ^ { x } & \leq y \leq 2 \end{aligned}$ Horizontal cross sections: $\begin{array} { c } 1 \leq y \leq 2 \ 0 \leq x \leq \ln 2 \end{array}$ D) Vertical cross sections: $\begin{aligned} 0 & \leq x \leq \ln 2 \ e ^ { x } & \leq y \leq 2 \end{aligned}$ Horizontal cross sections: $\begin{array} { c } 1 \leq y \leq 2 \ 0 \leq x \leq \ln y \end{array}$

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The region R is bounded by $y = e^x$ from below, $y = 2$ from above, and $x = 0$ from the left. The upper bound for $x$ comes from the intersection of $y = e^x$ and $y = 2$, which is at $x = \ln 2$. Therefore, for vertical cross sections, $x$ ranges from $0$ to $\ln 2$, and $y$ ranges from $e^x$ to $2$. For horizontal cross sections, $y$ ranges from $1$ (since $e^0 = 1$) to $2$, and $x$ ranges from $0$ to $\ln y$, since $x = \ln y$ is the inverse function of $y = e^x$.

Use Inequalities to Describe R in Terms of Its Vertical ex≤x≤20≤y≤ln⁡2\begin{aligned}e ^ { x } & \leq x \leq 2 \\0 & \leq y \leq \ln 2\end{aligned}ex0​≤x≤2≤y≤ln2​

Use Inequalities to Describe R in Terms of Its Vertical $\begin{aligned}e ^ { x } & \leq x \leq 2 \\0 & \leq y \leq \ln 2\end{aligned}$