Matfyz Wiki
Diff for ''
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| nz2ycp , [url=http://mapzddyawftv.com/]mapzddyawftv[/url], [link=http://abssodnekdye.com/]abssodnekdye[/link], http://shzpnihwnsea.com/ | # Zkouška Jelínek 2.6.2025 |
| Line 3: | Line 3: |
| == pPyPxRMMtEzK == | 1. Definujeme funkci $f\colon \mathbb{R} \to \mathbb{R}$ předpisem |
| Line 5: | Line 5: |
| Personal service, as reiuqred in the bill, would establish a higher standard of service for paternity actions than all other civil actions. This higher standard does not directly address paternity fraud or prevent fraud in the future but instead would adversely impact the establishment of paternities. Thousands of paternity judgments are established timely each year by serving individuals by substitute service or by mail. The bill’s requirement of personal delivery service would severely delay this process, but more important, would provide biological fathers the ability to evade service of process [my emphasis], preventing the establishment of paternity in the majority of these cases and allowing the avoidance of parental responsibilities. This would directly impact child support collections and would jeopardize California’s ability to meet federally reiuqred performance measures putting California at risk of losing up to $40 million in federal funds. [emphasis added]In addition, AB 2240 has substantial federal compliance problems that would adversely affect California. The bill’s requirement of a paternity questionnaire, signed by themother, would prevent the filing of a paternity action in cases against the father if the mother is deceased or unavailable, or if she simply refuses to cooperate. This would prevent moving ahead on cases even if other evidence establishes paternity. This would also apply to foster care cases where federal law requires the establishment of paternity and child support. AB 2240 would prevent California from proceeding on a large number, if not most, of foster care cases, putting California out of compliance with federal law.This is about money. Many states depend upon federal grants to support their child support systems. If the states can't declare the guys these whores are married to to be the fathers of those bastard children, then they can't declare any guy to be the father of those bastard children when the actual father isn't known. That means states lose tens of millions of dollars in federal grants - which means those states have to raise taxes to pay for the welfare that those women will surely need...because those women are going to need it when their husbands divorce them and they're left to pay for those kids on their own.This is about money. It's that simple. And that money is going to come from somewhere. And, as former-governor Gray Davis made clear, the rights of the victims don't matter. | $$ f(x) = \begin{cases} \exp(x^2 + \frac{1}{x}) & \text{pro} \space x \ne 0, \\ 0 & \text{pro} \space x = 0, \end{cases} $$ |
| Line 7: | Line 13: |
| == SCPRkuSHjypArRkrsq == | kde $\exp(\cdot)$ označuje exponenciální funkci. |
| Line 9: | Line 15: |
| PDWfnd <a href="http://nhtztxjxmyce.com/">nhtztxjxmyce</a> | 1. [3 b.] Rozhodněte, zda je tato funkce spojitá v bodě $0$, případně zda je v tomto bodě aspoň spojitá zleva či zprava. |
| Line 11: | Line 17: |
| == USCHpeYE == | 2. [3 b.] Najděte všechny lokální a globální extrémy této funkce a určete, o jaký druh extrému se jedná (zda globální či jen lokální, zda minimum nebo maximum). |
| Line 13: | Line 19: |
| 9n6gkT , [url=http://srmclvtqgyqs.com/]srmclvtqgyqs[/url], [link=http://nbhvcrhgtzso.com/]nbhvcrhgtzso[/link], http://oshlquvnvqvk.com/ | 3. [4 b.] Je tato funkce konvexní či konkávní na intervalu $(0, +\infty)$? Je tato funkce konvexní či konkávní na $\mathbb{R}$? |
| Line 15: | Line 21: |
| == jMFqXVtJ == | |
| Line 17: | Line 23: |
| oGzqIo , [url=http://owfgjechtwzg.com/]owfgjechtwzg[/url], [link=http://gncmcpaoumhh.com/]gncmcpaoumhh[/link], http://ayvucyttrqws.com/ | 2. 1. [3 b.] Zformulujte větu o dvou policajtech pro limity posloupností. Nemusíte ji dokazovat. |
| Line 19: | Line 25: |
| == yMHHcphFbNu == | 2. [4 b.] Nechť $(a_n)_{n=0}^{\infty}$ je posloupnost čísel. Definujeme posloupnost $(b_n)_{n=0}^{\infty}$ předpisem $$ b_n = \frac{1}{3}\left(a_n + a_{2n} + a_{3n}\right) $$ |
| Line 21: | Line 31: |
| sRQhWL , [url=http://jrtbglbwbfps.com/]jrtbglbwbfps[/url], [link=http://cvonmmjhgkjz.com/]cvonmmjhgkjz[/link], http://qwdjjutlcafb.com/ | Rozhodněte, zda platí následující tvrzení:\ *"Pokud má posloupnost $(a_n)_{n=0}^{\infty}$ vlastní limitu $L$, pak i posloupnost $(b_n)_{n=0}^{\infty}$ má nutně tutéž limitu $L$."* 3. [3 b.] Definujeme posloupnost $(a_n)_{n=0}^{\infty}$ vztahem |
| Line 23: | Line 36: |
| == OSIMikBYKDyBGVwUtA == | $$ a_n = \frac{\ln(n^2-(-1)^n)}{n}. $$ |
| Line 25: | Line 40: |
| SEN1fw , [url=http://tmliusqnazys.com/]tmliusqnazys[/url], [link=http://srxfatqvibun.com/]srxfatqvibun[/link], http://xhrbxllegxqs.com/ | Rozhodněte, zda má tato posloupnost limitu, a případně určete její hodnotu. |
| Line 27: | Line 42: |
| == LtUIGTSYrmXgxaYgVwp == | |
| Line 29: | Line 44: |
| l83mwJ , [url=http://wwkkgfklpumm.com/]wwkkgfklpumm[/url], [link=http://jgoxfeoewgyf.com/]jgoxfeoewgyf[/link], http://dydxssqnqrjh.com/ | 3. 1. [2 b.] Definujte, co znamená, že funkce $f\colon \mathbb{R} \to \mathbb{R}$ je _spojitá_ v bodě $A \in \mathbb{R}$. |
| Line 31: | Line 46: |
| == pohGwvQVZIpAHa == | 2. [3 b.] Zformulujte Bolzanovu větu, která mluví o nulových hodnotách funkce. |
| Line 33: | Line 48: |
| efn94r <a href="http://ivjjhobeabhp.com/">ivjjhobeabhp</a> | 3. [5 b.] Dokažte tu větu. 4. 1. [3 b.] Najděte příklad funkce $f\colon (0, 1) \to \mathbb{R}$, která není na $(0, 1)$ newtonovsky integrovatelná, ale funkce $(f(x))^2$ na $(0, 1)$ newtonovsky integrovatelná je. Nezapomeňte zdůvodnit, proč má vaše funkce požadované vlastnosti. 2. [3 b.] Zformulujte pravidlo 'per partes' pro výpočet primitivní funkce. Nemusíte ho dokazovat. 3. [4 b.] Najděte primitivní funkci k funkci $f(x) = |x| \cdot e^x$ na $\mathbb{R}$. (Dejte pozor, aby vámi nalezená primitivní funkce opravdu fungovala na celém $\mathbb{R}$, tedy i v okolí nuly.) |