Exercise 3. Consider the famous Fibonacci sequence \( \left\{x_{n}\right\}_{n=1}^{\infty} \), defined by the relations \( x_{1}=1, x_{2}=1 \), and \( x_{n}=x_{n-1}+x_{n-2} \) for \( n \geq 3 \) (a) Compute \( x_{20} \). \[ \quad x_{n}=\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}\right] \] (b) Use an extended Principle of Mathematical Induction in order to show that for (c) Use the result of part (b) to compute \( x_{20} \).

The exponential model \( \mathrm{A}=474.2 e^{0.006 t} \) describes the population, A , of a country in millions, \( t \) years after 2003 . Use the model to determine the population of the country in 2003 . The population of the country in 2003 was \( \square \) million.

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) d) Determine the symmetry of the graph. Odd; origin symmetry Even; \( y \)-axis symmetry Neither

A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 80 ft of fence? What is the maximum area of this garden? Select the correct choice below and fill in the answer box(s) to complete your choice. A. The area is maximized when both sides are \( \square \mathrm{nt} \). The area is maximized when the longer side is \( \square \mathrm{ft} \) and the shorter side is The maximum area that the farmer can enclose with 80 ft of fence is \( \square \mathrm{sq} \mathrm{ft} \)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-2} \) To graph the function, first determine the symmetry of the graph of f . Choose the correct answer below. y-axis symmetry origin symmetry neither \( y \)-axis symmetry nor origin symmetry What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.)

6) O domínio da função dada por \( \mathrm{f}(\mathrm{x})= \) é a) \( \{x \in R \mid-2 \leq x \leq 3\} \). b) \( \{x \in R \mid-2 \leq x<3\} \). c) \( \{x \in R \mid 2 \leq x<3\} \). d) \( \{x \in R \mid-2 \leq x \leq 3\} \). e) \( \{x \in R \mid x \neq 3\} \).