Tema
Q:
Given the following exponential function, identify whether the change represe
percentage rate of increase or decrease.
\[ y=990(1.922)^{x} \]
Q:
The domain of the function \( f(x) \) is \( [5,12] \) and the range is \( [-11,19] \). Using interval
find the domain and range of \( g(x)=-f(x) \).
Q:
1) Let \( z e t \)
find \( z^{3} \) in polar
form.
Q:
Graticar lafunción \( y=f(x)=3 x^{2}-5 x+2 \)
Q:
1. Esboce o gráfico das funções abaixo:
a) \( y=2 x^{2}+4 x+4 \)
Q:
\[ \text { Polynomial interpolation } \]
ercise 1 Let's the function \( f(x)=\sqrt{x} \).
1. Estimate the value of \( f \) in the point 115 , by using Lagrange interpolation if the
interpolation nodes are \( x_{0}=100, x_{1}=121, x_{2}=144 \).
2. Give a majorating of the committed error.
Q:
3 If \( f(x)=\log _{3} x \) and \( g(x) \) is the image of \( f(x) \) after a translation fiv
units to the left, which equation represents \( g(x) \) ?
\( \begin{array}{ll}\text { (1) } g(x)=\log _{3} x-5\end{array} \)
Q:
3.1. Find the binomial expansion of \( \left(x-\frac{1}{x}\right)^{5}, x \neq 0 \), simplifying each term of the
expansion.
3.2. Given \( \frac{1}{(4-x)^{2}} \),
3.2.1. Expand it in ascending powers of \( x \) as far as the term in \( x^{2} \).
3.2.2. What are the limits of \( x \) for which the expansion in 3.2 .1 is true?
3.3.1. Expand the binomial \( \sqrt{225+15 x} \) as an infinite series, up to and including the
term in \( x^{2} \).
3.3.2. By substituting \( x=1 \) in the expansion above, show that \( \sqrt{15} \approx \frac{1859}{480} \).
Q:
1. Soient \( (a, r) \in \mathbb{R} \times] 0,+\infty[ \). Traduire en termes d'intervalles les inégalités suivantes :
\[ |x-a| \leq r, \quad|x-a|>r \]
Q:
2.4. Write the polar equation \( r=\cos \theta+\sin \theta \), in Cartesian form, and hence
show that it represents a circle, further determining the coordinates of its
centre and the size of its radius.
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