If limit of function f(x)=(sin x-cos x)/cos 2x is l, choose the good answer:…

# If limit of function f(x)=(sin x-cos x)/cos 2x is l, choose the good answer:…

• CALCULUS

If limit of function f(x)=(sin x-cos x)/cos 2x is l, choose the good answer:…

We have to find the limit of f(x)=(sin x-cos x)/cos 2x for x–> 45 degrees. We know that cos 2x = (cos x)^2 – (sin x )^2 lim x–> 0 [(sin x-cos x)/cos 2x] => lim x–> 0 [(sin x-cos…

• TRIGONOMETRY1

What are sin x, tan x, cot x, if 180<x<270 and cos x=-4/5?

We have cos x = -4/5. Also 180< x< 270. For these values of x sin x is negative and so is cos x. We use the relation (cos x)^2 + (sin x)^2 = 1 => (-4/5)^2 + (sin x)^2 = 1 => (sin x)^2 =…

• MATH

For the complex number 3 + 4i, what is the absolute value and the argument? Is it not tan (4/3)?

A complex number z = x + yi, can be expressed as a line with a length equal to |z| or sqrt (x^2+ y^2). The line makes an angle A with the positive x-axis that is known as its argument and equal to…

• WILLIAM BUTLER YEATS

How did William Butler Yeats use extensive symbolism in “An Acre of Grass”?

In “An Acre of Grass,” Yeats’ speaker is an old man who believes that books are his “acre of grass.” Because he is an old man, he can no longer run around outside to keep fit; his “strength of…

• SILAS MARNER

In Silas Marner, what is Nancy’s reason for not agreeing to adopt a child?

It is important to remember that this novel is written in a very different time when people held (by our standards) very traditional religious views that shaped their outlook on life and on many…

• PHYSICS

What is the distance traveled by the car during the period of acceleration in the following…

The car was initially travelling at 80 km/h. It then accelerates at 12km/h^2 for 22 seconds. 22 seconds is equal to 22/3600 hours. Therefore the speed of the car after the period of acceleration…

• SOCIAL SCIENCES

Are the agents of socialization that affect you today the same as the ones that affected you…

I would imagine that, for most adults, the agents of socialization that affect us today are different from those that affected us earlier in our lives. This is because we are at a much different…

• THE CHRYSALIDS

Why is The Chrysalids written in a first-person narrative?

Let us consider the aspects of first-person point of view. Because of the intensely personal nature of the narrative, because after all we see everything through the eyes of one central character,…

• MATH

What is the absolute value of: (1 + i) (6 + 2i)/ (4 + i) (9 + 3i)

We have to find the absolute value of (1 + i) (6 + 2i)/ (4 + i) (9 + 3i). First we convert it to a form x+iy and then use the formula sqrt(x^2 + y^2) to determine the absolute value. (1 + i)(6 +…

• THE ODYSSEY

In order from start to finish, in Homer’s The Odyssey, did Odysseus travel starting in Troy and…

In Homer’s epic, The Odyssey, our hero, Odysseus, has left home years before to fight the war with the Trojans. In fact, Odysseus left his home in Ithaca twenty years prior to the beginning of this…

• HAMLET

What does the scene on the castle’s battlements in Shakespeare’s Hamlet, reveal about Prince…

At the beginning of William Shakespeare’s play, Hamlet, Horatio comes to Hamlet to tell him that Old Hamlet’s ghost has appeared on the battlements. Hamlet assures Horatio that he will join him…

• LAW AND POLITICS

Why did the Supreme Court declare some New Deal measures unconstituational ?

The major case in which the Supreme Court struck down a New Deal program was the case of Schechter Poultry Corporation v. United States (1935). In this case, the Court struck down the National…

• HAMLET

Do you think Hamlet and Ophelia are a good match in Hamlet?

For a textual answer to your question you could look at what both Laertes and Polonius say to Ophelia in Act 1 of the play. Laertes and Ophelia have an interesting conversation right before…

• EMILY DICKINSON

What is the thesis in, “If I can stop one heart from breaking,” by Emily Dickinson?

Emily Dickinson’s poem, “If I can stop one heart from breaking,” provides a clear insight into the kinds of things that the author genuinely cared about. Though she traveled very little from home,…

• HAMLET

In Shakespeare’s Hamlet, describe what happens to Polonius?

In Shakespeare’s play, Hamlet, one of the main characters is Polonius. Polonius is an advisor to the King who, ironically, has wise advice that he never takes himself, and who talks too much, while…

• CHEMISTRY

What is polythene? What are examples of sports materials made from polythene?

Polythene or Polyethylene or polyethene is a polymer made of units of ethene or ethylene. Ethene has the molecular formula C2H4 with the two carbon atoms linked together by a double bond as…

• HISTORY

What was it like for the individual soldier in Vietnam as it relates to his understanding of…

To my knowledge, there was not a problem with individual soldiers understanding what the rules of engagement were in Vietnam. The problem for soldiers in Vietnam was accepting these rules. The…

• BIOLOGY

What is hair toxicology. I need to write a research paper on various aspects related to it.

The correct terminology here would be the use of hair in toxicology. Toxicology is a study of the effects of chemicals on the human body. This can be done on people while they are alive or after…

• HISTORY

How did colonialism give rise to the Vietnam War?

Colonialism helped to give rise to the Vietnam War because it made the Vietnamese hate the French and want to overthrow them. The fact that the main resistance to the French was done by the…

• SCIENCE

Coordinate planeWhat is the coordinate plane?

When you think of a graph, you probably imagine a big plus sign. That is known as the coordinate plane, because it has an X axis and a Y axis and the point where the X and Y meet is known as a…

• SCIENCE

Factors that increase the risk of osteoporosisFactors that increase the risk of osteoporosis.

There are a lot of risk factors here, some of them behavioral and some of them that cannot be changed. If you want a full rundown on these, please follow this link:…

• APPLICATIONS

Viete formulasdiscuss Viete’s formulas

Viete’s relations make the connections between the coefficients of a polynomial and its roots. For instance, we’ll have a quadratic equations. ax^2 + bx + c = 0 We’ll write Viete’s relations: x1 +…

• CINEMA

What are the gothic elements of the Ridley Scott film Bladerunner?

What an excellent question! l had never considered the gothic elements in Blade Runner (or its parent novel, Do Androids Dream of Electric Sheep?) before, but it certainly fits most aspects of the…

• HISTORY

What would a person coming to America in the late 1700s, but before the Revolution, see when the…

Much is going to be dependent on where the boat docked. For example, if a boat docked in the Northern Colonies, I think that there were several components of colonial life that were distinct….

• SCIENCE

Vitamin C and fluIs vitamin C of any help in fluenza?

A lot of people believe that Vitamin C helps build your body’s resistance to flu and other viral illnesses. You can find lots of web sites that talk about using Vitamin C for this purpose….

• GEOMETRY2

Dimensions of rectangleif i know the vertices of rectangle , could i determine it’s dimensions ?

When given the vertices’s of rectangle, we can find the dimensions by using the distance between points formula. The distaqnce formula if given by : D = sqrt(x1-x2)^2 + (y1-y)^2 The formula you…

• SCIENCE

Increased amount of greenhouse gasesWhat happens when the amount of greenhouse gases is increasing ?

If the amont of greenhouse gases increases, average temperatures will rise, assuming that nothing else happens to counteract the effects of the gases. The greenhouse gases are called this because…

• HISTORY

How did people get around during the 1700s?I’m writing a story for history and I was wondering…

There are a couple of answers that could be correct here, depending largely on where your family lives. First of all, if the family lived in town, it would be very likely that the church would have…

• THE PIT AND THE PENDULUM

How do you analyze and interpret “The Pit and the Pendulum”?

Any interpretation of a given work of literature leaves itself open to massive debate, so I can present one of the central ways in which this classic horror story can be interpreted, but please do…

• SCIENCE

Scientific paperI need to find when sinx = sin2x. is it possible ?

Yes, it is possible for a range of values of x. To determine these values, we’ll have to solve the above equation. First, to emphasize the fact that we are talking about an equation, we’ll move the…

• TRIGONOMETRY MATH

Verify an inequality2sinx<cosx

If we’ll divide by cos x, we’ll get: 2 sin x/cos x < 1 2 tan x < 1 tan x < 1/2 Since the tangent function is not limited, this inequality is not holding for any value of x. I’ll suggest to…

• HEALTH ISSUES

TeaWhy is good to drink hot tea when you catch a flu?

The tea industry also claims that tea can help boost the strength of your immune system in general. They claim that theanine, an ingredient of tea, can help improve the performance of your immune…

• SCIENCE

Trigonometric functionsI try to determine cot x using right triangle but i don’t know where to…

We’ll start from Pythagorean theorem. According to the Pythagorean theorem in a right angle triangle: (sin x)^2 + (cos x)^2 = 1 If we’ll divide the expression by (sin x)^2, we’ll get: (cos…

• APPLICATIONS

Distance findingDiscuss how trigonometry is used to find the distance from a point to a line .

So, we have the equation of the line and a point, whose coordinates are known. The point is not on the given line. We’ll draw a parallel line to x axis, that is passing through the given point….

• APPLICATIONS

IntersectionHow to determine the equations of two lines that are intercepting ?

You can start from the intercepting point and the slope-intercept form of the equation of the line. y = mx + n The intercepting point is located on both lines. We know that when the lines are…

• APPLICATIONS

Slope directionDiscuss when the slope of a line is positive, negative, 0, or undefined.

In case of positive slope, y is increasing as x is increasing, so the lline is ascending to the right. In case of negative slope, y is decreasing as x is increasing, so the line is going down to…

• MATH

Who is responsible for math?who ever made Math I hate them and love them at the same time I don’t…

Mathematics texts have been found that are quite ancient. Babylonian texts from 1800 B.C. and Egyptian texts from 2000-1800 B.C. have been found. These texts have information about the Pythagorean…

• OCTOBER SKY

What is the most significant thing Homer Hickam does in October Sky?

I would say that the Homer’s pursuit of his dreams is probably the most significant element in his narrative. The fact that he never sacrifices his dream despite his father’s inertia and the state…

• LOOK HOMEWARD, ANGEL

What does the title Look Homeward, Angel mean?

The subtitle “The Story of a Buried Life” gives you one clue as to who the angel is. The angel of the title appears in the book in the form of a stone angel that Gant sells to Eliza to use for…

• SOCIAL SCIENCES

What was the proposal to privatize Social Security?

The most recent proposal to privatize Social Security was put forward by Pres. Bush in 2004 during his campaign for reelection. After being reelected, he put some effort into pushing his plan, but…

• PSYCHOLOGY AND COGNITIVE SCIENCES

Are you able to tell when someone is being honest with you?Are you able to tell when someone is…

Your question sounds more like it belongs in the psychology group because many theories have been advanced regarding such human behavior. There are documented physiological changes that occur when…

• THE GRAPES OF WRATH

What is the purpose of chapter 7?The Grapes of Wrath by John Steinbeck

Much like the newsreel style of John Dos Passos in U.S.A. Trilogy, Steinbeck’s intercalary Chapter 7 portrays rhetorically the cold exploitation of the used car salesmen who sell vehicles to the…

• THE GREAT GATSBY

In The Great Gatsby, how are Daisy and Gatsby similar and different? Can you support it with 4…

Well, Danielle, this actually is a little confusing. I can’t recall specific passages from the novel that directly compare or contrast Daisy and Gatsby, but various passages about Daisy and about…

• THE GIVER

Why is the relationship between Jonas and the Giver more dangerous compared to the other…

The relationship that Jonas has with The Giver is very different than his other relationships. All of Jonas’s other relationships revolve around careful behavior designed to keep distance…

• LAW AND POLITICS

In the following case, how did the prosecution get a RICO conviction?United States v. Fernandez,…

A defendant is guilty of conspiracy to violate § 1962(c) if the evidence shows that he or she knowingly agreed to facilitate a scheme that includes the operation or management of a RICO…

• THE CANTERBURY TALES

How would you compare and contrast the Pardoner to the Monk in The Canterbury Tales?

The main point of comparison would be in the way that Chaucer views them. The pardoner and the monk are both members of the clergy, an institution that Chaucer typically holds up for ridicule due…

• REFERENCE

Any suggestions how to update preprinted material?Hello all I want to amend some of my last…

I am assuming these are materials that you do not have an electronic copy of. If that is the case you can scan them into a computer with a scanner. There are several programs out there that will…

• WAITING FOR GODOT

what are the differences and common points in waiting for godot and heart of dearkness by J….

The characters in both seek out the meaning of life, after the readings and interpretations one can conclude that there is no meaning for life. Life is absurd.

• OTHELLO

How does the handkerchief function in act 4? Keeping track of its movements from here to the end…

Othello’s handkerchief that he had given to Desdemona before the play begins becomes the play’s most important prop and an ironic symbol of their relationship. The handkerchief actually comes into…