\( 16 d ^ { 4 } y / d x ^ { 4 } + 24 d ^ { 2 } y / d x ^ { 2 } + 9 y = 0 \)

Find the area of the region between the curve and the \( x \)-axis. \( f(x)=4-x^{2} \), from -6 to 6 The area is \( \square \) square units. (Type an integer or a simplified fraction.)

b) \( f(x)=-2 \sqrt[4]{x} \) a. \( \frac{2}{3} x^{\frac{-1}{3}} \) b. \( \frac{2}{3} x^{2} \) c. \( -2 \cdot \frac{1}{4} x^{\frac{-3}{4}} \)

Evaluate the \( \lim _{x \rightarrow-2}\left(\frac{x^{3}+6 x^{2}+8 x}{x+2}\right) \) Solution:

d) \( f(x)=-\frac{3}{s^{2}}-\frac{4}{s^{4}} \) a. \( 6 s^{-3}+16 s^{-5} \) b. \( 16 x^{4}+2 x \)

Sketch the region enclosed by \( y=e^{2 x}, y=e^{4 x} \), and \( x=1 \). Find the area of the region.