Outline the history of English drama, using “Ages” as a taxonomy.
- MATH
y=x2+x−−−−−√y=x2+x Sketch the curve by locating max/mins, asymptotes, points of inflection,…
y=x2+x−−−−−√y=x2+x a) Asymptotes Domain of function is x ≥≥ -2 Since the function has no undefined points , so it has no vertical asymptotes. Horizontal Asymptotes: Let’s find the limits of the…
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- MATH
y=1−x−−−−−√+1+x−−−−−√y=1-x+1+x Sketch the curve by locating max/mins, asymptotes, points of…
y=1−x−−−−−√+1+x−−−−−√y=1-x+1+x Domain of function: −1≤x≤1-1≤x≤1 a) Asymptotes a) Asymptotes The function has no undefined points, so there are no vertical asymptotes. For horizontal asymptotes , check…
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- MATH
y=x2x+8y=x2x+8 Sketch the curve by locating max/mins, asymptotes, points of inflection, etc.
y=x2x+8y=x2x+8 a) Asymptotes Vertical asymptotes are the zeros of the denominator x+8=0⇒x=−8x+8=0⇒x=-8 Vertical asymptote is x=-8 Degree of numerator=2 Degree of denominator=1 Degree of…
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- MATH
y=1×2−1(x−2)2y=1×2-1(x-2)2 Sketch the curve by locating max/mins, asymptotes, points of…
y=1×2−1(x−2)2y=1×2-1(x-2)2 To determine the asymptotes, express the function as a single fraction. Since the LCD of the two fractions is x^2(x-2)^2, then, the function becomes:
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- MATH
y=1x(x−3)2y=1x(x-3)2 Sketch the curve by locating max/mins, asymptotes, points of…
y=1x(x−3)2y=1x(x-3)2 a) Asymptotes Vertical asymptotes are the zeros of the denominator. x(x−3)2=0⇒x=0,x=3x(x-3)2=0⇒x=0,x=3 So, x=0 and x=3 are the vertical asymptotes. Degree of numerator=0 Degree of…
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- MATH
y=x1−x2y=x1-x2 Sketch the curve by locating max/mins, asymptotes, points of inflection, etc.
y=x1−x2y=x1-x2 a) Asymptotes Vertical asymptotes are the zeros of the denominator of the function. 1−x2=0⇒(1+x)(1−x)=01-x2=0⇒(1+x)(1-x)=0 x=−1,x=1x=-1,x=1 Vertical asymptotes are x=1 and x=-1 Degree of numerator=1…
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- MATH
y=x4−3×3+3×2−xy=x4-3×3+3×2-x Sketch the curve by locating max/mins, asymptotes, points of…
The function has no vertical, horizontal or slant asymptotes. You need to determine the extrema of the function, hence, you need to determine the zeroes of the first derivative:
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- MATH
y=x3−6×2−15x+4y=x3-6×2-15x+4 Sketch the curve by locating max/mins, asymptotes, points of…
y=x3−6×2−15x+4y=x3-6×2-15x+4 a) Asymptotes Polynomial function of degree 1 or higher can’t have any asymptotes. b) Maxima/Minima y’=3×2−12x−15y′=3×2-12x-15 y’=3(x2−4x−5)y′=3(x2-4x-5) y’=3(x−5)(x+1)y′=3(x-5)(x+1) Now we can find critical…
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- MATH
y=2−2x−x3y=2-2x-x3 Sketch the curve by locating max/mins, asymptotes, points of inflection,…
You need to evaluate the horizontal asymptotes to the graph of function, such that: limx→+∞2−2x−x3=∞limx→+∞2-2x-x3=∞ limx→−∞2−2x−x3=∞limx→-∞2-2x-x3=∞ Notice that the graph has no vertical or…
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- MATH
limx→(π2)−(tan(x))cos(x)limx→(π2)-(tan(x))cos(x) Evaluate the limit.
limx→(π2)−(tan(x))cos(x)limx→(π2)-(tan(x))cos(x) =limx→(π2)−ecos(x)lntan(x)=limx→(π2)-ecos(x)lntan(x) applying the limit chain rule, limx→(π2)−cos(x)lntan(x)limx→(π2)-cos(x)lntan(x) =limx→(π2)−⎛⎝lntan(x)1cos(x)⎞⎠=limx→(π2)-(lntan(x)1cos(x))…
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- MATH
limx→1+(xx−1−1ln(x))limx→1+(xx-1-1ln(x)) Evaluate the limit.
limx→1+(xx−1−1lnx)limx→1+(xx-1-1lnx) To evaluate the limit of this function as x approaches 1 from the right, assign values to x that is greater than 1, but very near 1. Then, plug-in that value to…
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- MATH
limx→π−(x−π)csc(x)limx→π-(x-π)csc(x) Evaluate the limit.
You need to evaluate the limit, hence, you need to replaceππ for x in expression under limit: limx→π(x−π)cscx=π−πsinπ=00limx→π(x-π)cscx=π-πsinπ=00 Since the limit is indeterminate 0000 , you…
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- MATH
limx→∞(x2−x3)e2xlimx→∞(x2-x3)e2x Evaluate the limit.
limx→∞(x2−x3)e2xlimx→∞(x2-x3)e2x =limx→∞x3(1x−1)e2x=limx→∞x3(1x-1)e2x Apply the Algebraic limit theorem, =limx→∞x3(limx→∞1x−1)limx→∞e2x=limx→∞x3(limx→∞1x-1)limx→∞e2x plug in the value of x…
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- MATH
limx→∞e4x−1−4xx2limx→∞e4x-1-4xx2 Evaluate the limit.
You need to evaluate the limit, hence, you need to replace ∞∞ for x in expression under the limit, such that: limx→∞e4x−1−4xx2=e∞−1−∞∞=∞∞limx→∞e4x-1-4xx2=e∞-1-∞∞=∞∞ Hence,…
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- MATH
limx→0e4x−1−4xx2limx→0e4x-1-4xx2 Evaluate the limit.
You need to evaluate the limit, hence, you need to replace 0 for x in expression under the limit, such that: limx→0e4x−1−4xx2=e0−1−00=1−10=00limx→0e4x-1-4xx2=e0-1-00=1-10=00 Hence, since…
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- MATH
limx→0tan(4x)x+sin(2x)limx→0tan(4x)x+sin(2x) Evaluate the limit.
You need to evaluate the limit, hence, you need to replace 0 for x in expression under the limit, such that: limx→0tan4xx+sin2x=tan00+sin0=00limx→0tan4xx+sin2x=tan00+sin0=00 Hence, since the…
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- MATH
limx→0ex−1tan(x)limx→0ex-1tan(x) Evaluate the limit.
You need to evaluate the limit, hence, you need to replace 0 for x in expression under the limit, such that: limx→0ex−1tanx=e0−1tan0=1−10=00limx→0ex-1tanx=e0-1tan0=1-10=00 Hence, since the…
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- MATH
f(x)=x2e−xf(x)=x2e-x Now to find the absolute extrema of the function , that is continuous on a closed interval, we have to find the critical numbers that are in the interval and evaluate the function at…
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- MATH
You need to evaluate the extreme values of the function on the interval [-pi,pi], hence, you need to evaluate the zeroes of the function f'(x). You need to find the derivative of the function:…
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- MATH
f(x)=x2+x+1−−−−−−−−−√,[−2,1]f(x)=x2+x+1,[-2,1] Find the local and absolute extreme values of the…
f(x)=x2+x+1−−−−−−−−−√f(x)=x2+x+1 Now to find the absolute extrema of the function , that is continuous on a closed interval, we have to find the critical numbers that are in the interval and evaluate the…
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- MATH
f(x)=3x−4×2+1,[−2,2]f(x)=3x-4×2+1,[-2,2] Find the local and absolute extreme values of the…
You need to evaluate the local absolute extrema of the function, hence, you need to find the zeroes of the equation f'(x) = 0. You need to evaluate the derivative using the quotient rule:
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- MATH
You need to evaluate the local absolute extrema of the function, hence, you need to find the zeroes of the equation f'(x) = 0. You need to evaluate the derivative using product rule, such that:…
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- MATH
f(x)=x3−6×2+9x+1,[2,4]f(x)=x3-6×2+9x+1,[2,4] Find the local and absolute extreme values of the…
f(x)=x3−6×2+9x+1,[2,4]f(x)=x3-6×2+9x+1,[2,4] Now to find the absolute extreme values of the function , that is continuous on a closed interval, we have to find the critical numbers that are in the interval and…
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- THE PIT AND THE PENDULUM
What is the setting of “The Pit and the Pendulum?”
This story is set during the Spanish Inquisition. This began in the late 15th century and lasted until the early 1800s. This story supposedly takes place in the early 1800s when Napoleon was in…
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- THE ODYSSEY
How is Odysseus loyal and brave? What is meant by an epic hero?
An epic hero is normally a character in a traditional epic or a work that emulates that genre. The heroes of epics are normally royal or noble, often with some sort of divine ancestry. They usually…
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- AN OCCURRENCE AT OWL CREEK BRIDGE
What is the turning point in “An Occurrence at Owl Creek Bridge” by Ambrose Bierce?
Ambrose Bierce’s story, “An Occurrence at Owl Creek Bridge,” includes many vivid details to depict a strong sense of place. The plot is driven by the action of the execution of Peyton Farquhar. The…
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- ROMEO AND JULIET
Romeo is impetuous; he is, at times, impulsive, at others, reckless. When he first meets Juliet, he falls instantly in love with her, and he wonders aloud, “Did my heart love till now?” (1.5.59)….
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- OF MICE AND MEN
In Of Mice and Men, what words and phrases does Steinbeck use in introducing readers to Curley…
In Of Mice and Men, Steinbeck establishes from the moment Curley, Lennie, and George encounter each other that there will be trouble. He offers a “cold” glance to George, but it is when his eyes…
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- SCIENCE
Are there any any decomposers in the ocean and what are they?
Decomposers are everywhere. On land, in both fresh and salt water, literally everywhere. Decomposers play an important role in the grand circle of life in that they return the nutrients,…
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- JODI PICOULT
What is the summary for The Pact by Jodi Picoult?
What an amazing book! I hope you enjoyed this read as much as I did! This is a story about love, friendship, morals, and tragedy. Chris and Emily are the main characters in the story. The two of…
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- OF MICE AND MEN
People believe that George killed Lennie for several reasons. Lennie accidentally killed Curley’s wife in the barn earlier. When Curley’s wife is killed, George knows that Curley will likely…
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- TO KILL A MOCKINGBIRD
Once Jem decides to tell Scout about retrieving his pants from the fence at the Radley place, he…
In Chapter 6 of To Kill a Mockingbird, Jem, Dill, and Scout decided to sneak into the Radleys’ yard in order to peek into the windows. The three had to crawl under a wire fence that surrounded the…
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- THE METAMORPHOSIS
In The Metamorphosis, who comes to live with the Samsas?
In the story “The Metamorphosis” by Franz Kafka, Gregor experiences a profound change that impacts his family. Throughout the story, Gregor works to support his family; however, after he…
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- LITERATURE
What do we mean by saying “language is rule-governed behavior”?
“Language is rule-governed behavior” means essentially that language only works if we follow its rules. Language exists for the purpose of communication, meaning that we must first agree upon what…
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- THE RAVEN
What is the narrator hoping the Raven can tell him?
The narrator sees the raven as some kind of prophet or omen. Lenore, someone who was dear to the narrator, presumably a lover, has recently died, and the narrator seeks answers to the questions…
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- HISTORY
Explain the power of judicial review under the U.S. Constitution.
The Constitution does not specifically set out the power of judicial review. However, it at least implies that the power exists. The Supreme Court formally took that power for itself in the 1803…
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- HISTORY
Why did Cubans declare independence from Spain?
Cuba declared its independence from Spain in 1895, as part of a revolution led by Cuban nationalist Jose Marti. Many Cubans had desired independence from Spain for years, and in fact the revolution…
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- OF MICE AND MEN
How does Steinbeck make the characters’ reactions to the dream of ‘livin’ off the fatta the lan’…
This is a great question. George and Lennie’s dream is powerful. From the beginning of the story, both men have a dream. They will live off the fat of the land and have a place to call home….
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- SCIENCE
What mass of O2 is needed to react with 10.2 grams of Fe?
The reaction of iron with oxygen can produce either FeOFeO or Fe2O3Fe2O3 , depending on the temperature and other conditions. I will show you the calculation for both. This is a stoichiometry…
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- 1984
What does Winston look for in the pub and in the room above Mr Charrington’s shop?
In Part 1, Chapter 8 of 1984, Winston follows an old man into a pub. As soon as he enters, he looks around for a telescreen: “It was horribly dangerous, but at any rate there was no telescreen in…
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- JULIUS CAESAR
How does Portia convince Brutus to disclose his secret to her? What do you think their…
Several Roman senators are plotting to kill Julius Caesar. They believe that he has too much power and is becoming dangerous. Brutus is asked to participate in the murder plot. He is torn between…
2 educator answers
- SOCIAL SCIENCES
Which role is more difficult in gender?
This is a great question, and one that feminist scholars, gender and sexuality scholars, sociologists, and anthropologists still debate! What makes this question so difficult is that it is largely…
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- THE CRUCIBLE
Why was Abigail dismissed from the Proctors’ service?
Elizabeth Proctor dismissed Abigail from service when her husband confessed to having an affair with Abigail. When Abigail and John Proctor speak in Act One, she says, “It’s she put me out, you…
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- SCIENCE
Does a compound has the same properties as the substances it contains?
Compounds are formed by chemical combination of two or more elements and contain a fixed ratio of these elements. Compounds can not be separated into constituent elements by physical means….
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- THE CRUCIBLE
In The Crucible, what reason does Abigail give Parris for being dismissed from the Proctors’…
In Act One, Abigail tells her uncle, Reverend Parris, that she was dismissed by Elizabeth Proctor because Elizabeth hates her as a result of the fact that “[Abigail] would not be her slave.” She…
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- BEOWULF
With what scene does the epic Beowulf open with?
Beowulf begins with a brief biography, and the death and burial, of Scyld Scefing (also called “Shield Sheafson” in some translations). We don’t learn much about Scyld, other than that he was a…
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- JANE EYRE
In chapter seventeen of Charlotte Bronte’s Jane Eyre, why did Jane leave the room where all of…
Chapter seventeen is the part in the novel where Mr. Rochester is using Ms. Ingram to incite jealousy in Jane and to see if Jane loves him. He may have honestly been considering Ms. Ingram for a…
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- MONSTER
What was Steve Harmon’s role in the robbery?
Steve Harmon’s role in the robbery was to act as the crew’s lookout. James King gave Steve the job of entering the drugstore beforehand to make sure that there weren’t any police officers or…
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- JANE EYRE
In what chapter do Mr. Rochester and Jane get married in?
In chapter twenty-six of Jane Eyre, Jane and Mr. Rochester begin their first marriage ceremony. As the minister is performing the ceremony, a strange man bursts into the church and interrupts. He…
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- LITERATURE
Outline the history of English drama, using “Ages” as a taxonomy.
Drama in English literary history can be followed by referring to more general periods, even in the English language itself. Earliest dramas were oral renditions of folk stories and moralities….
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