Homing pigeons avoid flying over water. Suppose a homing pigeon is released on an island at point \( C \), which is 11 mi directly out in the water from a point \( B \) on shore. Point \( B \) is 24 mi downshore from the pigeon's home loft at point \( A \). Assume that a pigeon flying over water uses energy at a rate 1.33 times the rate over land. Toward what point \( S \) downshore from A should the pigeon fly in order to minimize the total energy required to get to the home loft at A?

Evaluate the improper integral: \( \int_{1}^{\infty} \frac{1}{x^2} \, dx \)

Al resolver la integral doble \( \int_{0}^{2} \int_{0}^{1} x y \) dydx obtenemos: a. \( 4 / 3 \) b. \( 3 / 2 \) c. \( 1 / 3 \) d. \( 3 / 4 \)

Consider the parametric curve \( x=\cos \theta \) and \( y=\sin \theta \). Determine whether this curve is concave up, down, or neither at \( \theta=\frac{\pi}{6} \) A) upward B) downward C) neither D) All answers a b

4. DETERMINDR \( \quad \int^{\sqrt{4-x^{2}}} d x \).

If the point \( (1,2) \) is an inflection point of the curve of the function \( f \) where \( f^{\prime}(x)=4 x^{3}-\mathrm{k} x^{2} \), then \( \mathrm{k}=\ldots \ldots \) (a) 24 (b) 6 (c) 4 (d) 12