Question

A rectangle is to be inscribed under the arch of the curve $f(x) = \frac{3}{4}\sin(\frac{x}{2})$ from $x = 0$ to $x = 2\pi$. We wish to determine the dimensions of the rectangle with largest area, and its largest area. a. Formulate a function of the rectangle area. b. Apply properties of $\sin$ and the fact that $f(a) = f(b)$ to find a relation between a and b, where $0 \le a \le \pi \le b \le 2\pi$. c. Construct the area function $A(a)$ in terms of a only. Sketch $A(a)$ to show that the maximum of A is attained at $a \approx 1.420925$ Calculate the dimensions of the rectangle with largest area up to $10^{-6}$, and its largest area.

          A rectangle is to be inscribed under the arch of the curve $f(x) = \frac{3}{4}\sin(\frac{x}{2})$ from $x = 0$ to $x = 2\pi$. We wish to determine the dimensions of the rectangle with largest area, and its largest area.
a. Formulate a function of the rectangle area.
b. Apply properties of $\sin$ and the fact that $f(a) = f(b)$ to find a relation between a and b, where $0 \le a \le \pi \le b \le 2\pi$.
c. Construct the area function $A(a)$ in terms of a only. Sketch $A(a)$ to show that the maximum of A is attained at $a \approx 1.420925$
Calculate the dimensions of the rectangle with largest area up to $10^{-6}$, and its largest area.

A rectangle is to be inscribed under the arch of the curve f(x) = (3)/(4)sin((x)/(2)) from x = 0 to x = 2π. We wish to determine the dimensions of the rectangle with largest area, and its largest area.
a. Formulate a function of the rectangle area.
b. Apply properties of sin and the fact that f(a) = f(b) to find a relation between a and b, where 0 ≤ a ≤π≤ b ≤ 2π.
c. Construct the area function A(a) in terms of a only. Sketch A(a) to show that the maximum of A is attained at a ≈ 1.420925
Calculate the dimensions of the rectangle with largest area up to 10^-6, and its largest area.

Added by Erica E.

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