Approximation of f(x)

Because the new code starts with S = 1 and then keeps adding terms where the numerator is multiplied by X·X and the sign changes (multiplication by −1), it is generating the even-power alternating series.

So the function being approximated is the cosine series (Maclaurin series):

\(\displaystyle f(x) \approx \cos(x) = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\cdots\)

General term:
\(\displaystyle \cos(x)\approx \sum_{k=0}^{m}(-1)^k\frac{x^{2k}}{(2k)!}\) (up to the number of terms used in the loop).

Exam line: The loop computes an alternating even-power factorial series, hence it approximates \(\cos(x)\).

Deadlock in databases occurs when two or more transactions wait indefinitely for each other to release locks. There are three basic techniques to control deadlocks:
1) Deadlock Prevention:
This technique ensures that deadlock never occurs by eliminating one of the necessary conditions of deadlock.

• Request all required locks at once (no Hold and Wait).
• Impose ordering of resources.
• Use timestamp-based schemes (Wait-Die, Wound-Wait).

2) Deadlock Avoidance:
The system checks whether granting a lock will lead to a deadlock state.

• Uses algorithms like Banker’s Algorithm.
• Allocates resources only if the system remains in a safe state.

3) Deadlock Detection and Recovery:
Deadlocks are allowed to occur, but the system detects and resolves them.

• Use Wait-For Graph to detect cycles.
• Abort or roll back one or more transactions to break the deadlock.