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Calculus: Two Important Theorems – The Squeeze Theorem and Intermediate Value Theorem

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Learn about two very cool theorems in calculus using limits and graphing! The squeeze theorem is a useful tool for analyzing the limit of a function at a certain point, often when other methods (such as factoring or multiplying by the conjugate) do not work. This theorem also has other names like the Sandwich Theorem or the Pinch Theorem, but it is most commonly called the Squeeze Theorem. The Intermediate Value Theorem, often abbreviated as IVT, deals with a single function unlike the Squeeze Theorem.

Calculus: Limits vs Continuity with Explanations, Practice Questions, and Answers [AP Calculus, Calculus 101, Math]

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In the last two articles, we talked about limits and their application in determining the continuity of a function. Here, we will apply those skills to few practice questions. Attempt the problems on your own at first; however, if you get stuck, the solution to each problem is just below it. These problems vaguely range from easy to hard. Enjoy!

History of Tea and Modern Afghan Tea Culture

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When the term tea culture comes up, people usually think of places like Japan, China, or England, though perhaps Afghanistan deserves to be in this lineup too. While not as well known as those already mentioned, Afghanistan’s tea culture is a venerable one that dates back centuries. As with many ancient cultural artifacts, tea came to Afghanistan by way of the Silk Road, likely via merchants going to or from China. This tradition continues to this day, as while the country does grow some of its own tea, the majority of Afghanistan’s tea consumption relies on imports from China and Pakistan.

Alberto Santos-Dumont vs The Wright Brothers: Giants of Aviation

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Back in 2016, Rio de Janeiro hosted the Summer Olympics. The opening ceremony featured bossa nova, capoeira, and laser-lit choreography depicting key points in Brazil’s history. Among these theatric renditions was a curious biplane aviator that the Olympic announcer noted Brazilians claim to have beaten the Wright Brothers in their claim to fame. Are there any merits to this assertion? Has history snubbed this Brazilian inventor?

Greek Goddess Athena Facts & Mythology: Who was Athena the Goddess of?

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Fun Facts and Greek Mythology about Athena the Goddess of Wisdom. In this lesson, we learn all about our beautiful and wise Greek goddess Athena. Athena, also known as Pallas Athena or the Virgin Athena, is the celebrated goddess of wisdom, courage, inspiration, civilization, law and justice, strategic warfare, mathematics, strength, strategy, the arts, crafts, and skill in ancient Greek mythology. She is the daughter of Zeus and Metis, and is said to have been born fully grown and armored from the head of her father. The beautiful and wise Athena is one of the twelve most important Olympian deities who reside on Mount Olympus, alongside the handsome Greek Gods such as Hermes, Aphrodite, and Apollo.

History 101: What Are The 4 Causes of World War 1?

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An international conflict during the 1910’s, World War 1, was contributed by not one factor but numerous factors that led to its extensive atrocity. The aggressive rise and continuation of nationalism throughout countries greatly contributed to the start and four-year length of the war. In addition, the heightened race of militarism and its advanced trench warfare also contributed to the massive scale of the war, including the appalling losses of men as well as the elongated duration. Therefore, both the rise of nationalism, the patriotic feelings of countries’ people to fight, and the pursuit of militarism, advancements of armies, weaponry, and warfare style, played key roles in the contribution of the international conflict World War 1.

Margaret Chase Smith’s Speech of a Lifetime

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The American experiment was founded on the idea of a democracy where the people hold the ultimate power over the government. But when the government oversteps its power; when it threatens to endanger individual rights, it takes someone with true courage to stand up for the America public. Some of the most striking examples of blatant abuse of power in the last century occurred during the Cold War. From 1947 to 1991, the Capitalist United States (US) and the Communist Union of Soviet Socialist Republics (USSR) clashed in a series of escalating economic and political tensions. In the midst of this tumultuous period, US government officials became concerned that communist sympathizer would collude with Soviet spies and endanger national security. The most vocal advocate for the “Red Scare” was Republican Senator Joseph McCarthy of Wisconsin. McCarthy came under the national spotlight during his speech in Wheeling, West Virginia, when he claimed that 205 State Department employees were known communist infiltrators (Achter). Although he lacked definitive evidence to back his claim, McCarthy continued a long string of accusations against celebrities, politicians, and nearly anyone who disagreed with him. McCarthy’s campaign to “expose” communist infiltrators caused innocent Americans to lose their careers and reputations, and fueled McCarthy’s rise to power. This period of mass, unsubstantiated paranoia eventually became known as “McCarthyism” (Achter). Few dared to challenge him, for fear of becoming his next target; At least not until a woman by the name of Margaret Chase Smith stepped into the political fray.

From Warrior Footwear to High Fashion: The Origin of Heels

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The earliest recorded instance of heeled shoes comes from tenth century Persia. Mounted soldiers wore shoes with heels to make it easier to keep their feet in their stirrups, as the heels would catch the back of the stirrup’s tread and stop their feet from sliding in and out. This same use can be seen to this day with cowboys and other jobs that involve riding horses. During this period heels went from being a masculine sign of strength and wealth to a non-gendered court fashion to a feminine fashion statement.

Greek God Poseidon Facts & Mythology: Who was Poseidon the God of?

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Fun Facts and Greek Mythology about Zeus the God of the Seas and Storms. In this lesson, we learn all about Poseidon, a prominent god in Greek mythology, often associated with the sea, earthquakes, and horses. As an important figure in ancient Greek religion, Poseidon has left an indelible mark on Western culture. Poseidon is often depicted as a powerful and imposing figure, wielding a trident and riding on the backs of horses. He is the god of the sea and all its creatures, and is said to have the power to create and control waves, storms, and earthquakes. In mythology, Poseidon is also known for his temperamental nature and his penchant for punishing those who displease him. In addition to Poseidon, the beautiful Aphrodite and wise Athena are among the twelve most important Olympian deities who reside on Mount Olympus, alongside Greek Gods such as Hermes and Apollo.

Freddy Mamani’s New Andean Architecture

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Most artistic movements are named after the fact, often by critics, to group together the works of artists that share certain characteristics or that are in reaction to specific events and thus coincide thematically. Counter to this academic pattern is la nueva arquitectura andina (or the New Andean Architecture). The term was coined by the style’s creator: Freddy Mamani Silvestre, who goes by Freddy Mamani professionally.

Greek Goddess Aphrodite Facts & Mythology: Who was Aphrodite the Goddess of?

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Fun Facts and Greek Mythology about Aphrodite the Goddess of Love and Beauty. In this lesson, we learn all about our beautiful and charming Greek goddess Aphrodite. Aphrodite was the ancient Greek goddess of love, beauty, and sexuality. She was widely worshipped and considered one of the twelve Olympian gods and goddesses. Aphrodite was said to have been born from the foam of the sea, which is why she was often associated with the sea and seafaring people. She was known for her unparalleled beauty and grace, which earned her the title of the goddess of love and beauty. Her beauty was so captivating that it caused the gods and mortals alike to fall in love with her. The beautiful Aphrodite and wise Athena are among the twelve most important Olympian deities who reside on Mount Olympus, alongside Greek Gods such as Hermes and Apollo.

Interesting Facts About Phosphorus: Applications and Uses

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You can probably find that phosphorus is the 15th chemical element if you look at a periodic table. You might also easily guess that it has the chemical symbol P. But what you may not know is that beyond these basics, there are many different applications of phosphorus that make it a significant part of our everyday lives.

Come learn about interesting factors about phosphorus with us!