For a sequence formula_8, the similar notation formula_9 is used.
Imagine we have a function that takes an input, formula_6, and then outputs formula_11 to formula_12. If we were to draw a graph using x and y as coordinates, the results would look like this:
As we can see here, division by zero is undefined. But if we look closer, then we can see that we still have valid output—as long as we never reach zero:
This problem is unique to zero as the function still works on every value up to zero, even if we approach from the negative side. As input numbers get arbitrarily small, the output will simply get arbitrarily large, and if we draw this on a graph, the line will stretch upwards without bound before it touches 0 on either axis.
One way we describe this is "The limit of formula_13 as formula_6 approaches 0, from the right side, is formula_15", meaning that formula_13 can keep increasing beyond bounds, as long as "x" doesn't reach 0. Mathematically, this is written as: formula_17.
While a limit cannot be reached, it can be approached to get a more accurate output value. For example, the mathematical constant formula_18 (Euler's number) can be found by calculating formula_19, where formula_20 is an input:
While the equation will never be equal to formula_18, putting in a larger input will get us closer to it, and make our output more accurate. Mathematically, we can express this by saying that "The limit of formula_22 as formula_20 approaches formula_15 is formula_18", which is noted as formula_26.
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"Mario Sports Mix" features five sports: volleyball, field hockey, ice hockey, dodgeball, and basketball. Each sport features special moves that the characters can use. Both local and online multiplayer can be played. The game features characters from the "Mario", "Final Fantasy", and "Dragon Quest" series. Players can also play as their Mii characters.
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Colman first came to prominence for her supporting role as Sophie Chapman in the Channel 4 comedy series "Peep Show" (2003–2015). Her other TV comedy roles include "Green Wing" (2004–2006), "Beautiful People" (2008–2009), "Rev." (2010–2014) and "Twenty Twelve" (2011–2012). She also played various roles in "That Mitchell and Webb Look" (2006–2008), alongside her "Peep Show" co-stars David Mitchell and Robert Webb. Colman's move to drama saw her receive critical acclaim for her performance in Paddy Considine's film "Tyrannosaur" (2011). Her other film roles include PC Doris Thatcher in "Hot Fuzz" (2007), Carol Thatcher in "The Iron Lady" (2011), Queen Elizabeth in "Hyde Park on Hudson" (2012), Bethan Maguire in "Locke" (2013), Margaret Lea in "The Thirteenth Tale" (2013), Marion in "Tale of the Brave" (2014) and the Hotel Manager in "The Lobster" (2015). Colman will portray Queen Elizabeth II in the third and fourth season of the original Netflix series "The Crown".
A three-time BAFTA TV Award winner, she won Best Female Comedy Performance for "Twenty Twelve" and Best Supporting Actress for "Accused" in 2013, before winning Best Actress in 2014 for her role as DS Ellie Miller in the ITV crime series "Broadchurch". Colman was also nominated for the International Emmy Award for Best Actress for "Broadchurch". For her performance in the AMC/BBC miniseries "The Night Manager", she won the Golden Globe Award for Best Supporting Actress – Series, Miniseries or Television Film and was nominated for the Primetime Emmy Award for Outstanding Supporting Actress in a Limited Series or Movie.
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Lacey was born on 28 September 1935 in Harrow, London, England. He studied at the Harrow Weald Grammar School and at the London Academy of Music and Dramatic Art. Lacey was married to Mela White from 1959 until they divorced in 1971. Then he was married to Joanna Baker from 1972 until they divorced in 1991. He had three children. Lacey died on 15 May 1991 from liver failure cause by his liver cancer in London, England, aged 55.
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Barkley was born in Keytesville, Missouri. Her father was a lawyer. Her mother was a pianist who had studied in Europe. She married her first husband, Carleton Hadley, in 1931. She met him at Washington University in St. Louis, Missouri. He became a prominent railroad attorney. They had two daughters. He died in 1944 at the age of 42.
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