(a) \( \sum_{n=1}^{\infty} 2\left(\frac{4}{3}\right)^{n-1} \)

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

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

Realiza la investigación encome Integrar: de resolver los ejercicios: 1. \( \int x^{3} \cdot e^{x} d x \) 2. \( \int|1-x| \cdot \sqrt{x} d x \) 3. \( \int \frac{3 x}{\sqrt[3]{x^{2}+3}} d x \)

\( \int \sqrt[ \infty ] { x ^ { r } } d x \)

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.)