Topic
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.
Q:
\( \left\{ \begin{array} { l } { u _ { 0 } } \\ { u _ { n + 1 } = \frac { u _ { n } } { 2 } + 1 , \forall n \geq 0 } \end{array} \right. \)
Q:
4) Realizar el anailisis completo (dominio, imagen, asintotas, raiz, ordenada) y
graficar la aiguiente funcion:
\[ \begin{array}{ll}y=\frac{3 x-2}{2 x-3} & \text { Dar conjunto de positividad y negatividad. }\end{array} \]
Q:
Diseases tend to spread according to the exponential
growth model. In the early days of AIDS, the growth factor
(i.e. growth multiplier not growth rate) was around 2.2. In
1983, about 2000 people in the U.S. died of AIDS. If the
trend had continued unchecked, how many people would
have died from AIDS in 2003?
people
(Note: once diseases become widespread, they start to
behave more like logistic growth, but don't worry about
that for the purpose of this exercise)
Q:
- Find the maximal sampling period for to avoid the aliasing.
\[ x(t)=\sin (4000 \pi t) \]
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
