Explanation

Explanation

On January 25, 2024, Microsoft reached a $3 trillion market capitalization for the first time.

It became the second company ever to achieve this milestone after Apple in 2022.

Microsoft briefly surpassed the mark during intraday trading, joining the $3 trillion club.

Explanation

The derivative of 2^(-x) is -2^(-x) * ln(2), which can be written as -2⁻ˣ·log2 (considering log as ln or log base e implicitly in the derivative formula).

Explanation

The formula ∂f/∂x = lim(h → 0) [f(x + h, y) - f(x, y)]/h represents the partial derivative of f with respect to x, and it's evaluated at the point (x, y).

The answer is x at (x, y).

Explanation

Jannik Sinner (Italy) won the 2024 Australian Open Men’s Singles.

He defeated Daniil Medvedev in a five-set final: 3–6, 3–6, 6–4, 6–4, 6–3.

It was Sinner’s first Grand Slam title.

He became the first new Australian Open champion since 2014.

Explanation

Step 1: Evaluate the integral

∫(x² - x - 1) dx = (x³ / 3) - (x² / 2) - x

Step 2: Apply the limits of integration

[(1³ / 3) - (1² / 2) - 1] - [((-1)³ / 3) - ((-1)² / 2) - (-1)]

= [(1/3) - (1/2) - 1] - [(-1/3) - (1/2) + 1]

Step 3: Simplify the expression

= (1/3) - (1/2) - 1 + (1/3) + (1/2) - 1

= (2/3) - 2

= (2/3) - (6/3)

= -4/3

Explanation

Every subgroup of a cyclic group is also cyclic.

This is a key result in group theory under abstract algebra.

Explanation

Total ways to draw 3 balls = C(15, 3) = 455

Ways to draw 3 red balls = C(5, 3) = 10

Probability = 10/455 = 2/91

Explanation

The phrase "accede to" means to agree or consent to a request or wish.

"My Friend will accede to my wishes in this matter."

میرا دوست اس معاملے میں میری خواہشات پر عمل پیرا ہوگا۔

Explanation