En un diseño de red, se estima que un cable va a realizar un recorrido similar al de una parábola que se describe mediante la ecuación \( y=x^{2} \) desde \( x=0 \) hasta \( x=3 \) Encontrar la longitud total del cable para realizar el recorrido estimado.

Find Relative Extreme values of \( F(x)=2 x^{3}-9 x^{2}-24 \)

Calculate the area under the curve defined by the function \( f(x) = x^3 + 2x - 1 \) from \( x = 1 \) to \( x = 3 \).

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. \( e^{1-5 x}=851 \) The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is \{ (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Определите характер поведения функции \( y=x^{7}-x \).

Find relative Extreme values of \( F(x)=\frac{1}{4}-x^{3}-3 x \)