Abstract: This paper introduces the formal proof of the three mean value theorems of differentiation in detail. The differential mean value theorem is the core theorem of differential calculus, an ...

The Environmental Protection Agency has stopped estimating the dollar value of lives saved in the cost-benefit analyses for new pollution rules. Los Angeles smog in 1979. For decades, government ...

WAR, short for Wins Above Replacement, estimates how many additional wins a player contributes to their team compared to a readily available replacement-level player. By combining offense, defense, ...

Two sisters navigate the challenge that comes with their estranged father (Stellan Skarsgård) wanting to make a film about their private family life. We first meet close-knit sisters Nora (Worst ...

McDonald's franchisees worldwide will soon be assessed on how their prices deliver value, according to memos obtained by CNBC. The burger chain has leaned into value to appeal to cash-strapped diners ...

After years of trailing their hard-charging rivals in the information-technology sector, stocks from the so-called old economy are enjoying a moment of bliss. On Wednesday, the Dow Jones Industrial ...

Few filmmakers are as attuned as Joachim Trier to the inner lives of young people. In superb movies like Reprise, Oslo, August 31st and The Worst Person in the World, he has probed the artistic dreams ...

If you have kids, you’ve probably heard them blurt out “6-7” recently, with emphasis on the seven. Something like six-seven. Gen Alpha are randomly repeating the numbers and laughing at the inside ...

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The AI industry has a new buzzword: “PhD-level AI.” According to a report from The Information, OpenAI may be planning to launch several specialized AI “agent” products, including a $20,000 monthly ...

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics. In the fall of 1915, the foundations of physics ...