Numerade

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Zhumagali Shomanov

Numerade educator

Problem 1. (20 points) Find the following limits a) ( lim _{x ightarrow 3} frac{x^{2}-x-6}{x^{2}-9} ) b) ( lim _{x ightarrow 1} frac{sqrt{x^{2}+3}-2}{x-1} )

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Aparna Shakti

Numerade educator

Problem 2. (20 points) Find the following derivatives a) f(x) = 2x^5 - 5x^3 + 7x - 8 b) f(x) = (x^3 + 1) / (x^3 - 1) c) f(x) = ln(x^3 + 2x)

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Zhumagali Shomanov

Numerade educator

Find the equation of the tangent line to the curve y = 2x² - 1 at (1, -3).

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Zhumagali Shomanov

Numerade educator

Problem 5. (20 points) Let ( f(x)=x^{2}-5 x+12 ) a) Find critical points of ( f(x) ). b) On what intervals ( f(x) ) is increasing and decreasing? c) Find local maximum and local minimum of ( f(x) )

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Sanchit Jain

Numerade educator

Question # 2 (a) ACID properties are important principles of database technology. But NOSQL database follow BASE properties. How these set of principles differ? Elucidate your answer briefly.

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Shu Naito

Numerade educator

(b) The two tables 'Guest' and 'Celebrations' are created using the SQL statements given below. 1. CREATE TABLE Guest (guestname VARCHAR(30) PRIMARY KEY, arrival DATE NOT NULL, departure DATE NOT NULL); 2. CREATE TABLE Celebrations (celebname VARCHAR(30) PRIMARY KEY, start_date DATE NOT NULL, finish_date DATE NOT NULL); What result will be produced after executing the following SQL statement, or will there be an error? Explain your answer. 'SELECT guestname, 'sarrival duration', celebname FROM Guest, Celebrations WHERE arrival BETWEEN start_date AND finish_date;'?

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Sheryl Ezze

Numerade educator

Question # 1 (a) A specific operation applied to relations A and B will yield relation C as depicted below. [Marks:5] Please provide details about the SQL operation that produces relation C. A Sal_ID Prod_ID 110 1035 123 2518 239 2241 239 2518 337 2249 110 2249 239 2249 239 1035 B Prod_ID Name 1035 Sugar 2241 Tea 2249 Milk 2518 Milo C Sal_ID Prod_ID Name 110 1035 Sugar 123 2518 Milo 239 2241 Tea 239 2518 Milo 337 2249 Milk 110 2249 Milk 239 2249 Milk 239 1035 Sugar

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Shu Naito

Numerade educator

(b) Consider the following SQL statement. SELECT * FROM employee WHERE surname LIKE 'P__ris' AND department_no IS NOT NULL ORDER BY salary, employee_no; What output does this query produce? Question # 5 (a) Explain the fundamental concept of functional dependencies, including how they define relationships between attributes in a relational database schema. Elucidate your answer in five sentences. (b) Given the relational model below, normalize it to 3NF. Make sure you list the Functional Dependencies along with each relation and include all relations (each relation with its functional dependencies) in the summary. Customers (CID, FirstName, LastName, Email, Address, Company, CompanyInfo) FD1: CID ? FirstName, LastName, Email, Address, Company, CompanyInfo FD2: Company ? CompanyInfo

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Shu Naito

Numerade educator

Question # 5 (a) Consider the following three scenarios involving distributed database systems and transactional databases. For each scenario, indicate whether the principles of the CAP theorem or the ACID properties are more relevant, and provide your justification. i. Scenario: A company operates a real-time messaging platform where users expect instant message delivery, even in the event of network partitions. However, ensuring consistency across all distributed nodes is not a top priority. Is the CAP theorem or ACID properties more applicable in this scenario? ii. Scenario: A banking application processes financial transactions, such as deposits and withdrawals, where data integrity and consistency are paramount. It is essential to maintain accurate account balances and prevent unauthorized access or data corruption. Is the CAP theorem or ACID properties more applicable in this scenario? iii. Scenario: A social media platform allows users to post updates, photos, and comments, which are replicated across multiple data centers for redundancy and scalability. It is acceptable for users to experience eventual consistency, where data may temporarily diverge across different nodes. Is the CAP theorem or ACID properties more applicable in this scenario?

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Sheryl Ezze

Numerade educator

1) Find the first derivative f'(x). (10 points) a) f(x) = x^4e^x, b) f(x) = x^2/(1+2x). 2) Find the absolute maximum and absolute minimum values of f on the given interval. (10 points) f(x) = 12 + 4x - x^2, [0, 5]. 3) Evaluate the integral ?_2^5 (4 - 2x)dx. (10 points) 4) Use the Midpoint Rule, ?_a^b f(x)dx ? (b - a)f((a+b)/2), for numerical calculation of the integral. (10 points) ?_0^1 (x^3 - 3x^2)dx. 5) Complex numbers. Evaluate the expression and write your answer in the form a + bi. (2 points) a) (1 - 2i)(8 - 3i), b) (3 + 2i)/(1 - 4i).

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Xojimurod X.