b) \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{2} \sin x-1}{2 \cos ^{2} x-1} \)

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

Set up the definite integral required to find the area of the region between the graph of \( y=13-x^{2} \) and \( y=24 x+148 \) over the interval \( -5 \leq x \leq 3 \).

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. \( \int \frac{3 x}{\sqrt[3]{x^{2}+3}} d x \)

Set up the definite integral required to find the area of the region between the graph of \( y=16-x^{2} \) and \( y=-2 x-47 \) over the interval \( -3 \leq x \leq 7 \).

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.)