How are unicellular and multicellular organisms the same? How are they different?

The obvious differences in size and complexity between unicellular organisms such as bacteria and multicellular organisms such as animals obscure some more fundamental similarities. While a bacterium is a single cell that reproduces on its own and a large animal may consist of trillions of cells working together to reproduce, they are nonetheless both made of cells, and much of the functioning of those cells is shared between them. They all process nutrients, most of them breathe oxygen (anaerobic bacteria don't), and they all strive to survive and reproduce their DNA.

Multicellular organisms are all eukaryotes, while unicellular organisms can be either eukaryotes or prokaryotes. Eukaryote cells are much more complex, containing a nucleus and a variety of organelles such as mitochondria and lysosomes, while prokaryotes are much simpler and contain very little inner structure. In fact in many ways mitochondria themselves are basically prokaryotic organisms; they have their own DNA which is passed on differently. There is evidence that mitochondria actually emerged by ancient eukaryotic cells absorbing prokaryotic organisms into themselves.

Eukaryotic unicellular organisms are in some ways more similar to multicellular organisms than they are to prokaryotes; all the same basic cellular structures are already in place in a unicellular eukaryote such as the amoeba. To get from a prokaryote like E. coli to an amoeba you have to evolve a nucleus and a Golgi apparatus and transport proteins and so on; but put a whole bunch of amoeba together, and you sort of have a multicellular organism.

Indeed, that's basically what slime molds are; they straddle the line between unicellular and multicellular, consisting of many cells that join and split at different phases of their life cycle. But all these cells are basically the same.

The ancestor of all multicellular organisms was probably something like a slime mold; then at some point, hundreds of millions of years ago, it evolved the capacity to specialize its cells, making some perform different functions from others, despite having the same underlying DNA. (Think about all the different types of cells you have: brain cells, eye cells, skin cells, stomach cells, and so on; all of those cells share the same DNA, yet function quite differently.) That evolutionary innovation is possibly what made multicellular organisms as we know them possible.

How is African culture influenced in Chinua Achebe's novel 'Things Fall Apart'?

The second part of the novel focuses mainly on this aspect. It becomes clear that the arrival of the missionaries, obviously of European descent, and the establishment of foreign forms of government creates conflict not only between the colonialists and the tribes but also within the different villages, their inhabitants, their families and amongst individuals. It also gradually eroded the natives' convictions. It is this conflict and erosion which directly impact traditional culture and lead to its breakdown.

The arrival of a few white people created confusion amongst the natives, but the matter was quickly dealt with after consultation with the oracles, as Obierika tells Okonkwo in Chapter 15, when he went to visit him in exile:

"...The first people who saw him ran away, but he stood beckoning to them. In the end the fearless ones went near and even touched him. The elders consulted their Oracle and it told them that the strange man would break their clan and spread destruction among them..."

"...I forgot to tell you another thing which the Oracle said. It said that other white men were on their way. They were locusts, it said, and that first man was their harbinger sent to explore the terrain. And so they killed him."

The murder resulted in severe retribution by the white men, as Obierika explained further:

"...The three white men and a very large number of other men surrounded the market. They must have used a powerful medicine to make themselves invisible until the market was full. And they began to shoot. Everybody was killed, except the old and the sick who were at home and a handful of men and women whose chi were wide awake and brought them out of that market."

When Obierika returned for another visit, two years later, he told Okonkwo that the situation in his home village, Umuofia had changed drastically. The missionaries had built a church there and had already converted some of the inhabitants and were sending evangelists around to the other villages.

The missionaries also arrived in Mbanta and criticized the villagers' belief in dead gods of wood and stone who unfairly punished those who did not obey the rules and destroyed children. They were told of the holy trinity and the evangelists then burst into song, which enthralled many of the onlookers, especially Nwoye, Okonkwo's son.

Many of the villagers left and some of them mocked the new religion. However, an impact had been made and would later have serious repercussions on traditional life, since many of those who had been banished from their tribes would turn to the religion. Many converts would also be found in others, such as Nwoye, who had been affected by some or other painful trauma related to their own religion or culture.

When the missionaries were given land in the Evil Forest, many thought they would die, but they persevered and nothing happened to them. It was believed that they had a very powerful fetish and more converts were won. In this way, the missionaries gained more support, creating greater division amongst the villagers. The culture and beliefs of the natives were gradually being eroded in this manner.

The colonialists also introduced a new form of government and installed District Commissioners who introduced and exercised new laws. Certain cultural practices were outlawed, such as abandoning newborn twins in the evil forest. The perpetrators were arrested and imprisoned and were forced to perform menial tasks under guard. More serious crimes were punished by hanging. This form of control had a slow and debilitating effect on the villagers, which caused even more people to turn to the new faith, giving up their tradition.

Another factor which won many new converts, specifically in Umuofia, was the kindness and patience of Mr. Brown, the white missionary. He made the villagers believe that there was some value in the new faith, after all. He built a school and hospital in the village and, as the extracts below indicate, he won more and more support.

In the end Mr. Brown's arguments began to have an effect. More people came to learn in his school, and he encouraged them with gifts of singlets and towels.

And it was not long before the people began to say that the white man's medicine was quick in working.

It is in these ways that support for the white man's laws and his religion grew. Okonkwo was one of very few who saw the threat of the destruction of their culture. He was prepared to fight for his culture, but most did not have his fiery passion or conviction and gradually, Ibo culture was swallowed by a new belief system and a new government.

Okonkwo's suicide symbolizes the death of Ibo culture. He killed himself not only out of pride but also because he was not prepared to be dominated and ruled by something he could never accept. He would rather commit an abomination than commit to one.

Explain how Mary Maloney, Patrick, the detective, the unborn child, the leg of the lamb could be the 'lamb to the slaughter.'

The title of the story suggests that there is more than one meaning implied. It could be a double-entendre, or a triple-entendre (if there is such a thing), or a quadruple-entendre. Patrick is a big, tough cop, but he is the most obvious "lamb" to the slaughter because he actually is slaughtered. And he is slaughtered like an innocent lamb because he has no idea what is going to happen to him. He is innocent in another sense. He doesn't understand his wife at all--so he doesn't suspect that it is a bad idea to have his back turned to her, especially at that juncture.

Mary is very much like a lamb, at least up until the time that she succumbs to a fit of rage and bashes her unsuspecting husband over the head with the frozen leg of lamb. She is meek, mild, innocent, trusting, passive, and totally naive. It almost seems as if her whole world is her little house, the neighborhood grocery story, and the restaurant to which her husband takes her once a week. She trusts in Patrick like a little lamb--until he tells her what is on his mind.

The frozen leg of lamb, which is the centerpiece of the story, could be "the lamb to the slaughter" because it actually is a lamb and because it actually goes to the slaughter of Patrick Maloney. Without the leg of lamb there would probably have been no slaughter. Mary would not have gone to seek a weapon. She only committed the deed because she happened to have the perfect weapon in her hand.

The unborn child is like a lamb because, like a lamb, it is a baby. It is curled up peacefully inside its mother's womb. It is completely innocent. Nevertheless, it plays an important part in the "slaughter" of its father, for if Mary were not six months pregnant, and if she were not looking forward to motherhood and a happy domestic life, she probably would not have reacted to her husband's rejection with such savage rage. 

So Mary, Patrick, the unborn baby, and the frozen leg of lamb are not just "likely suspects" but are all simultaneously involved in the "slaughter" of Patrick Maloney. The choice of the title is brilliant. It is also comical, which is characteristic of Roald Dahl. Being funny, the title suggests that the whole story is not to be taken too seriously. The reader can't help being amused by the picture of a woman killing her husband with a frozen leg of lamb, and the reader can't help being amused by the final scene in which Mary gets the policemen to devour the incriminating evidence.

How does Shakespeare present the character of Lady Macbeth and establish the potential for future conflict in Act I, Scene 5 of Macbeth?

In Act I, Scene 5, Lady Macbeth receives a letter from her husband describing his encounter with the witches and their prophecy that he will become king of Scotland. She is presented as a devoted wife, willing to abandon whatever scruples she has to help her husband achieve what they view as his destiny. When she discovers King Duncan will be at their castle, she immediately resolves to "unsex" herself, becoming ruthless and cruel in order to push Macbeth, who she views as "too full of the milk of human kindness" to carry out the murder that will put him on the throne. She is also remarkably assertive. No sooner does she learn Duncan will be staying at Inverness that night then she begins to hatch a plan to kill him. She tells Macbeth what to do, advising him to greet Duncan with great hospitality so as not to reveal their plot:

bear welcome in your eye,
Your hand, your tongue; look like the innocent flower,
But be the serpent under't.

Beyond that, she tells Macbeth, he should "leave the rest to me," meaning Macbeth should simply act normal while she plans the brutal and treasonous murder of the king. Lady Macbeth's actions would have been viewed by Shakespeare's audiences as not only devious and cruel, but as an inversion of the natural order of things. This is certainly how she is presented in this scene, and it is consistent with the theme originally described by the witches: what's fair is foul and what's foul is fair. Yet the modern audience might be equally struck by Lady Macbeth's love and ambition for her husband as well as her willingness to defy prescribed gender roles. As for the potential for conflict, it is obvious the couple is plotting to kill the King, an act that will plunge Scotland into bloody chaos.

How does Macbeth discuss what it means to be human and have a conscience?

Macbeth is fully aware of his conscience. Guilt and fear occur to him almost immediately after he considers killing the king. He must really work up to killing Duncan. His wife encourages him but in the end, he must psyche himself into a mental state to overcome his fear and future guilt. At the end of Act I, Scene 4, Macbeth has not yet killed Duncan. But he is already trying to hide his murderous thoughts: 

Stars, hide your fires; 

Let not light see my black and deep desires. 

The eye wink at the hand; yet let that be

Which the eye fears, when it is done, to see. (I.iv.57-60) 

He doesn't want the stars shed light on his evil thoughts. He is afraid for the "eye" to see what he is thinking and what he might do. One could interpret that Macbeth is afraid of what God or other people think of him. But this idea of hiding his guilt has to do his own conscience. It's as if he doesn't want his own "eye" (mind or conscience) to see or acknowledge the evil that he is considering. So, to be human, is to wrestle with one's own urges and ethics. This is a Freudian analysis in the sense that Macbeth is wrestling with his own superego and Id: his respective reason and "deep desires." Macbeth feels at the mercy of a war between his conscience and his desires. 

Because Macbeth never masters his urges and emotions, he blames fate and circumstance. He feels more like a puppet than a person. He is never able to use his free will and conscience to override his urges. Therefore, he concludes that his free will had been an illusion. Here is part of his famous nihilistic quote in Act V, Scene 5: 

Life's but a walking shadow, a poor player 

That struts and frets his hour upon the stage 

And then is heard no more. It is a tale 

Told by an idiot, full of sound and fury, 

Signifying nothing. (V.v.26-30) 

Macbeth feels like an actor. His life had been scripted and therefore his own will has meant nothing. Having never mastered his own reason and desires, in the end he feels like life is simply a matter or being manipulated. 

`f(x) = arctan(e^x)` Find the derivative of the function

The given function: `f(x) =arctan(e^x)`  is in a form of inverse trigonometric function.

It can be evaluated using the derivative formula for inverse of tangent function:

`d/(dx)arctan(u) = ((du)/(dx))/(1+x^2)` .

 We  let `u = e^x` then  `(du)/(dx)= d/(dx) (e^x)= e^x` .

Applying the the formula, we get:

`f'(x)= d/(dx) arctan(e^x)`

          `=e^x/(1 +(e^x)^2)`

Using the law of exponent: `(x^n)^m=x^(n*m)` , we may simplify the part:

`(e^x)^2 = e^((x*2)) = e^(2x)`

The derivative of the function` f(x) = arctan(e^x)` becomes:

`f'(x)= e^x/(1 +e^(2x)) ` as the Final Answer.

In "The Umbrella," what kind of woman is Madame Oreille?

In the story, Madame Oreille is a miserly woman. Her chief preoccupation in life is to save money, and she is a tyrant to her husband in this regard. Monsieur Oreille is hardly allowed to have any pocket money at all, and he lives in constant fear of his wife's shrewish temper.

Although Madame Oreille and her husband have no children and can live comfortably, Madame Oreille's fear of future want prevents her from fully enjoying her present circumstances. The author describes Madame Oreille as a "little woman of about forty, very active, rather hasty, wrinkled, very neat and tidy, and with a very short temper."

Madame Oreille's short temper is frequently trained on her husband. When Monsieur Oreille protests that he is tired of using the cheap and flimsy umbrella she bought to replace his old one, Madame Oreille becomes angry. She eventually buys him a new, more expensive one, albeit accompanied by a lecture that it will not be replaced in a hurry if his new one is ruined through carelessness on his part.

As time progresses, Monsieur Oreille's umbrella is soon mysteriously found to be burned in different places. As for his part, Monsieur Oreille cannot explain how the burns occurred. Madame Oreille, furious at her husband, refuses to replace the umbrella. There is a stalemate between the two until a family friend advises Madame Oreille to seek compensation from their fire insurance company.

Madame Oreille is reluctant to do so initially, but she soon relents. In the conversation between Madame Oreille and the insurance men, Madame Oreille is seen to be a calculating opportunist, who will resort to fabrications in order to save herself the expense of replacing a ruined umbrella; she is quite happy for her husband to have a newer, sturdier umbrella if someone else will foot the costs for what she considers a frivolous expense.