... this limit is called the derivative of y with respect to x, evaluated at x = x0. The derivative of y with respect to x, at x = x0, may be interpreted as the slope of the tangent AT, and this slope is defined as the slope of the curve y = f (x) at x = x0. Further, the derivative of y with respect to x, at x = x0, may be interpreted ... similarly designated. Every application of differential calculus stems directly or indirectly from one or both of the two interpretations of the derivative as the slope of the tangent or curve and as the rate of change of the dependent variable with respec...

• Word Count: 2379
• Approx Pages: 10
• Grade Level: High School

... velocity x' and the vertical velocity y' were the fluxions of x and y associated with the flux of time. The fluents or flowing quantities were x and y themselves. With this fluxion notation y'/x' was the tangent to f(x,y) = 0. In his 1666 paper Newton discusses the converse problem, given the relationship between x and y'/x' find y. For that reason the slope of the ... tangent was given for each x and when y'/x' = f(x) then Newton solves the problem by antidifferentiation. He also calculated areas by antidifferentiation and this work contains the first clear statement of the Fundamental...

• Word Count: 1603
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

...  of Archimedes' spiral with inversion circle of radius 1 at center is the reciprocal spiral.   Archimedes' spirals as inverse to each other. The yellow curve is the inversion circle.   Nested Tangent Circles The tangent circles of Archimedes's spiral are all nested.   Because there is a linear relation between radius and the angle, the distance between the windings is constant. There are two classical mathematical ... ...

• Word Count: 1264
• Approx Pages: 5
• Grade Level: High School

... artist before or after them, the Beatles hold the record for most number one singles by any act. Twenty of the Beatles singles reached number one on the charts and most stayed for more than twelve weeks. In fact, combined, the original Beatles albums (not including the Anthologies) have spent a total of 147 weeks ... at number one on the charts. So the truth lies in the numbers. The Beatles we all know consisted of a four man operation including: John Lennon, Paul McCartney, George Harrison, and Richard ... a final budget of $1,250,000, was released by United Artists, along with the sou...

• Word Count: 1627
• Approx Pages: 7
• Has Bibliography
• Grade Level: High School

... 1965. In the year 1966, after Pickett covered it, the song became number six in the R&B charts of US and number twenty three in the Pop charts. It turned out number four in the same year for Canada's RPM charts and number twenty eight in the United Kingdom's singles chart. As Rosenthal (2013) points out, one ... 1966. The song was the first label of an independent group to appear on national billboards and pop charts, and it managed to peak to top ten in the list. It was the biggest hit on R&B magazine charts, remaining number one in the list for some weeks. When a vocal crew, referred t...

• Word Count: 1806
• Approx Pages: 7
• Has Bibliography
• Grade Level: High School

... RCA records. Their first big hit was in Germany with the song, "I Want You Back." By February of 1998, this song was all over the top 40 charts. In March of "98 their first album, "N Sync, was released. With help from a concert video shown on the Disney Channel and the emerging popularity of clean ... their trophy selves at home. But by January of 2000, their album was certified 10x platinum, and their new single "Bye Bye Bye" hit the top 40 charts. At the end of March of 2000, "N Sync's nest LP, No Strings attached was released. An unprecedented 4 million copies were shipped into stored...

• Word Count: 1605
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

... historic moments in the now booming rap industry. One of hip-hop's first prominent female acts, Salt-N-Pepa hit the top twenty of Billboard's pop-charts with "The Show Stoppa" in 1985 and "Push It" in 1987 (Ogg, 109-110). Another groundbreaking female was Queen Latifah, who stormed the ... single broke the top ten. Furthermore, their debut album, License to Ill hit number one, becoming the first rap record to peak the Billboard charts (Ogg, 88-89). The crowning moment of rap however took place when Run-DMC and Aerosmith released their collaboration of "Walk This Way." The ... hybrid betw...

• Word Count: 2030
• Approx Pages: 8
• Has Bibliography
• Grade Level: High School

... first release. Lewis' remake of Roy Hall's "Whole Lotta Shakin' Goin' On" spent twenty three weeks on the top of the country charts, going all the way to number one, and topping out at number three on the pop charts. The fallow up single and probably his most well known single "Great Balls of Fire", also went to the number one spot ... , and subsequent singles "You Win Again" and "Breathless" were in the top ten on the country charts. While on the road, Jerry spent a lot of time parting he picked a lot of bad habits like extreme binge drinking. Lewis was known as a wild man and doing off...

• Word Count: 2378
• Approx Pages: 10
• Has Bibliography
• Grade Level: High School

... manslaughter on November 7, 2011, later receiving a four-year prison sentence. At the age of 13, Jackson launched a solo career in addition to his work with the Jackson 5. He made the charts in 1971 with "Got to Be There" from the album of the same name. His 1972 album, Ben, featured the eponymous ballad about a rat. The song became Jackson's first solo ... out on his own more. Teaming up with rock legend Paul McCartney, Jackson sang on their 1982 duet, "The Girl Is Mine," which nearly reached the top of the pop charts.The song also appeared on his next solo album, Thriller (1982), whic...

• Word Count: 1265
• Approx Pages: 5
• Grade Level: High School

... August 1969, the Jackson 5 was introduced to the music industry at an event, and became an opening act for the Supremes. Their first album Diana Ross Presents the Jackson 5 hit charts in December of that year. The first single, "I Want You Back," hit number 1 on the Billboard Hot 100 chart in January 1970. Many more chart-topping singles similar ... ; and "I'll Be There" (Michael Jackson Biography). At the young age of 13, Michael Jackson started a solo career in addition to his role in the Jackson 5. He made charts in 1971 with "Got to Be There" from the album under the same name (The B...

• Word Count: 1568
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

... sure the two colors are very different. For instance, you can switch from a dark brown to light green, just not from a dark brown to dark green. With data visualization like charts, choose the correct color, always add a pattern or texture to different parts of chart. This will make it easier for visual difference. Use high contrasting colors, implement patterns, apply symbols ... three colors, green, red and blue. After reading about color blindness, I know that people with color blindness just skip over pie charts, they avoid them at all cost, especially if the colors on the chart are...

• Word Count: 1624
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

Pop Rock has been around for decades with different cultural bands across the world. Back in the 1960's a British Pop Rock group from Liverpool hit top charts and number one hit singles with their albums. This band was named The Beatles. They visited many countries and cities on tour all over the world. They put a big impact ... lot of number one hits like "Love Me Do," "From Me To You," and "She Loves You." All of these hit singles went straight to number one on single hit charts. Also their album "Please Please me" went to number one on the top selling album chart. These hit singles and al...

• Word Count: 1272
• Approx Pages: 5
• Grade Level: High School

... never accepted as a female singer in the mid-60's. In 1970, Wagoner suggested she record a cover of Jimmie Rodger's "Mule Skinner Blues". The single shot to number three on the charts and started Dolly's solo career. She left her duet partner and struck out as a soloist and in 1974; she recorded her first number one single "Jolene". - From 1974-1980, Dolly ... recorded a duet with Tammy Wynette - "Two Story House" - Also in 1980, George recorded a number one single "He Stopped Loving Her Today" which pushed him back to the top of the charts and helped him begin a series of Top 10 hits a...

• Word Count: 1281
• Approx Pages: 5
• Grade Level: High School

... impressed and described the boy as a "wonder". He was signed to Motown and was renamed "Little Stevie Wonder". His song "Fingertips, Part 2" reached the number one spot on the pop charts and the album this song was on; titled 12 Year Old Genius became the first Motown album to reach the number one spot on the pop album ... charts. Also in 1962, Berry Gordy formed a jazz label called Workshop Jazz. He started this label to convince the most talented jazz musicians in Detroit, to play on his pop music ... Berry Gordy. The Jackson Five from Gary, Indiana, were signed to Motown. Four of t...

• Word Count: 1447
• Approx Pages: 6
• Grade Level: High School

... as characterized by exaggerated muscularity. He was the predecessor and inspiration for the artistic movement called Vitalism, which sought to externalize the internal life forces in everything. I go on this tangent because looking at a work from Rodin, which is inherently immobile, but evocative of so much energy, I feel that I can align myself with Rilke's description of his experience of the sculpture ... ...

• Word Count: 1507
• Approx Pages: 6
• Grade Level: High School

... an anchor weighing down the human race from advancing intellectually, and an excuse for some to not even attempt advancement. It is grossly over- assuming and lacks any kind of tangent basis. " Christianity has been the most calamitous kind of arrogance yet." (Cowan 75). It has allowed men without any kind of proper qualifications run rampant across the globe proclaiming to ... ...

• Word Count: 2488
• Approx Pages: 10
• Has Bibliography
• Grade Level: High School

... that stop your body from exiting the circle of motion tangentially. At any one point in the ride the inertia of your body "wants- it to exit the circle at a tangent to the circle but the walls of the ride exert a centripetal force against your body stopping it. The normal force can become very strong. This force can be many Gs ... ...

• Word Count: 1272
• Approx Pages: 5
• Has Bibliography
• Grade Level: High School

... , in the 1870's James Starley began to manufacture bicycles in Britain. He developed the high-wheel bicycle which became popular throughout Europe. He also developed spoked wheels and the cross-tangent method of spoking which is still in use today (Whitt 13-14). This made bicycle wheels lighter and easier to keep true. Other important developments around this time were the ... ...

• Word Count: 2028
• Approx Pages: 8
• Grade Level: High School

... book, which shows an instability in his life. Many secrets were withheld, why, probably for the sanctuary of his own well being. De Quincy really starts to go off on a tangent nearing the end of the book, he goes on to explain his dreams. The one thing that gets me is the crocodile that haunts him in his sleep, any time ... ...

• Word Count: 1578
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

... desires he not only cannot but is polite about it, he is still completely under the control of society. The next morning when Marla comes downstairs, she goes off on a tangent about the bridesmaid dress she is wearing. How it was used for one day then tossed aside. It seems to be a cry from her for more affection from him outside ... ...

• Word Count: 2448
• Approx Pages: 10
• Grade Level: High School

... different areas of postmodern concept. Welsh's book "Marabou Stork Nightmares" challenges convention in the way it is presented which I thought was very effective. The way the text was presented on a tangent to signify the varying levels of consciousness the main character was experiencing. Overall, I do believe that postmodernism cannot be anything other than a good thing. However, my criticism of postmodernism is ... ...

• Word Count: 1591
• Approx Pages: 6
• Grade Level: High School

... sobbing husband. She does not face him seriously and even calls him a wrong name. In opposition to the anesthesiologists, hand surgeons help people to live a hopeful life, because hands provide a tangent force to the real word. Dr. Ovita cares about the people and the war in Israel and actually motivates other doctors to voluntarily go there. I believe he knows the importance ... ...

• Word Count: 1580
• Approx Pages: 6
• Grade Level: High School

... with the best life possible. To get a better handle on this subject I found an article from Men's Health titled "Are you a money moron?" It was written by Richard Sine and published October of 2013. I located this source on June 15th, 2015 on the library database, EBSCO host under the very first link. There is a quiz directly in the article ... ...

• Word Count: 1364
• Approx Pages: 5
• Grade Level: High School

... her to change his men back to normal. During their argument, Odysseus said "How dare you tell me to treat you with warmth? You, who turned my men into sine in your own house now you hold me here as well- teeming me with treachery, you lure me to your room to mount your bed". This shows that Odysseus ... ...

• Word Count: 1524
• Approx Pages: 6
• Grade Level: High School

... self. Maggie represents herself as an ugly duckling because of the scars from the fire. "She has been like this, chino n her chest, eyes on ground, feet in shuffle, ever sine the fire that burned the other house to the ground " (Walker811). The scar left Maggie resentful of her sister because of the trouble life she endures growing up. Maggie becomes ... ...

• Word Count: 1723
• Approx Pages: 7
• Has Bibliography
• Grade Level: High School