# limx→0sin−1(x)xlimx→0sin-1(x)x Find the limit. Use l’Hospital’s Rule where appropriate. If…

**MATH**

**limx→0sin−1(x)xlimx→0sin-1(x)x Find the limit. Use l’Hospital’s Rule where appropriate. If…**

Given the limit limx→0sin−1(xx)limx→0sin-1(xx) . We have to find the limit. Applying the limit we get, limx→0sin−1(xx)=limx→0sin−1(1)=π2limx→0sin-1(xx)=limx→0sin-1(1)=π2 hence the limit is π2π2

1 educator answer

**MATH**

**limx→0x−sin(x)x−tan(x)limx→0x-sin(x)x-tan(x) Find the limit. Use l’Hospital’s Rule where…**

limx→0x−sinxx−tanxlimx→0x-sinxx-tanx Apply L’Hospital’s rule. =limx→01−cosx1−1cos2x=limx→01-cosx1-1cos2x Apply L’Hospital’s rule again. =limx→0sinx−2sinxcos3x=limx→0sinx-2sinxcos3x Cancel sinx.sinx….

1 educator answer

**MATH**

**limx→0tanh(x)tan(x)limx→0tanh(x)tan(x) Find the limit. Use l’Hospital’s Rule where appropriate….**

First transform the expression: tanh(x)tan(x)=sinh(x)cosh(x)sin(x)cos(x)=(sinh(x)sin(x))⋅(cos(x)cosh(x)).tanh(x)tan(x)=sinh(x)cosh(x)sin(x)cos(x)=(sinh(x)sin(x))⋅(cos(x)cosh(x)). The second fraction obviously has limit 1 when x→0x→0, and we can omit…

1 educator answer

**MATH**

**limx→0sinh(x)−xx3limx→0sinh(x)-xx3 Find the limit. Use l’Hospital’s Rule where…**

Given the limit function limx→0sinh(x)−xx3limx→0sinh(x)-xx3 Applying the limits we have, limx→0sinh(x)−xx3=00limx→0sinh(x)-xx3=00 Using L’Hospital’s rule we get, limx→0cosh(x)−13×2=00limx→0cosh(x)-13×2=00…

1 educator answer

**MATH**

**limx→0ex−1−xx2limx→0ex-1-xx2 Find the limit. Use l’Hospital’s Rule where…**

Given the limit function limx→0ex−1−xx2limx→0ex-1-xx2 . We have to find the limit. We can see that the above limit is of the form 0000 . So we have to apply L’Hospital’s rule. i.e. differentiating…

1 educator answer

**MATH**

**limu→∞eu10u3limu→∞eu10u3 Find the limit. Use l’Hospital’s Rule where appropriate….**

You need to evaluate the limit, hence, you need to replace ∞∞ for u: limu→∞eu10u3=e∞∞=∞∞limu→∞eu10u3=e∞∞=∞∞ Since the limit is indeterminate ∞∞∞∞ , you may apply l’Hospital’s…

1 educator answer

**MATH**

**limx→01+2x−−−−−−√−1−4x−−−−−−√xlimx→01+2x-1-4xx Find the limit. Use l’Hospital’s Rule…**

limx→01+2x−−−−−−√−1−4x−−−−−−√xlimx→01+2x-1-4xx =limx→0(1+2x−−−−−−√−1−4x−−−−−−√)(1+2x−−−−−−√+1−4x−−−−−−√)x(1+2x−−−−−−√+1−4x−−−−−−√)=limx→0(1+2x-1-4x)(1+2x+1-4x)x(1+2x+1-4x) =limx→0(1+2x)−(1−4x)x(1+2x−−−−−−√+1−4x−−−−−−√)=limx→0(1+2x)-(1-4x)x(1+2x+1-4x)…

1 educator answer

**MATH**

**limt→08t−5ttlimt→08t-5tt Find the limit. Use l’Hospital’s Rule where appropriate….**

limt→∞8t−5ttlimt→∞8t-5tt Apply L’Hospital rule, Test condition:0/0 =limt→∞(8t−5t)’t’=limt→∞(8t-5t)′t′ =limt→∞(8tln(8)−5tln(5))=limt→∞(8tln(8)-5tln(5)) plug in the value, =80ln(8)−50ln(5)=80ln(8)-50ln(5) =ln(8)−ln(5)=ln(8)-ln(5)…

1 educator answer

**MATH**

**limt→1t8−1t5−1limt→1t8-1t5-1 Find the limit. Use l’Hospital’s Rule where…**

limt→1t8−1t5−1limt→1t8-1t5-1 =limt→1(t−1)(t+1)(t2+1)(t4+1)(t−1)(t4+t3+t2+t+1)=limt→1(t-1)(t+1)(t2+1)(t4+1)(t-1)(t4+t3+t2+t+1) limt→1(t+1)(t2+1)(t4+1)(t4+t3+t2+t+1)limt→1(t+1)(t2+1)(t4+1)(t4+t3+t2+t+1) plug in the value,…

1 educator answer

**MATH**

**limx→∞ln(x−−√)x2limx→∞ln(x)x2 Find the limit. Use l’Hospital’s Rule where…**

limx→∞lnx−−√x2limx→∞lnxx2 Apply L’Hospital rule , Test L’Hospital condition:∞∞∞∞ =limx→∞(lnx−−√)'(x2)’=limx→∞(lnx)′(x2)′ =limx→∞(1x√)(12)(x−12)2x=limx→∞(1x)(12)(x-12)2x…

1 educator answer

**MATH**

**limx→0+ln(x)xlimx→0+ln(x)x Find the limit. Use l’Hospital’s Rule where appropriate. If…**

You need to evaluate the given limit, such that: limx→0+lnxx=ln0+0+limx→0+lnxx=ln0+0+ limx→0+lnxx=(−∞)⋅10+limx→0+lnxx=(-∞)⋅10+ limx→0+lnxx=−∞⋅(+∞)=−∞limx→0+lnxx=-∞⋅(+∞)=-∞Hence,…

1 educator answer

**MATH**

**limx→∞x+x21−2x2limx→∞x+x21-2×2 Find the limit. Use l’Hospital’s Rule where…**

limx→∞x+x21−2x2limx→∞x+x21-2×2 limx→∞x2(1x+1)x2(1×2−2)limx→∞x2(1x+1)x2(1×2-2) limx→∞1x+11×2−2limx→∞1x+11×2-2 apply infinity properties, =0+10−2=−12=0+10-2=-12

1 educator answer

**MATH**

**limx→∞ln(x)x−−√limx→∞ln(x)x Find the limit. Use l’Hospital’s Rule where appropriate….**

limx→∞ln(x)x−−√limx→∞ln(x)x Apply L’Hospital rule , Test L’Hospital condition:∞∞∞∞ =limx→∞(ln(x))'(x−−√)’=limx→∞(ln(x))′(x)′ =limx→∞1x(12)(x−12)=limx→∞1x(12)(x-12) =limx→∞2x−−√=limx→∞2x…

1 educator answer

**MATH**

**limθ→(π2)1−sin(θ)csc(θ)limθ→(π2)1-sin(θ)csc(θ) Find the limit. Use l’Hospital’s…**

limθ→π21−sinθcscθlimθ→π21-sinθcscθ The function 1−sinθcscθ1-sinθcscθ is defined at θ=π2θ=π2 . So to take its limit, there is no need to apply the L’Hospital’s Rule. Instead,…

1 educator answer

**MATH**

**limθ→(π2)1−sin(θ)1+cos(2θ)limθ→(π2)1-sin(θ)1+cos(2θ) Find the limit. Use…**

You need to evaluate the limit, hence, you need to replace pi/2 for theta in limit, such that: limθ→π21−sinθ1+cos2θ=1−sin(π2)1+cosπlimθ→π21-sinθ1+cos2θ=1-sin(π2)1+cosπ…

1 educator answer

**MATH**

**limx→0x21−cos(x)limx→0x21-cos(x) Find the limit. Use l’Hospital’s Rule where…**

limx→0x21−cos(x)limx→0x21-cos(x) The function f(x)=x21−cosxf(x)=x21-cosx is undefined at x=0. So to compute its limit as x approaches zero, apply the L’Hospital’s Rule. Take the derivative of the…

1 educator answer

**MATH**

**limt→0e2t−1sin(t)limt→0e2t-1sin(t) Find the limit. Use l’Hospital’s Rule where…**

You need to evaluate the limit, hence, you need to replace 0 for t in the limit, such that: limt→0e2t−1sint=e0−1sin0=1−10=00limt→0e2t-1sint=e0-1sin0=1-10=00 Since the limit is indeterminate…

1 educator answer

**MATH**

**limx→0sin(4x)tan(5x)limx→0sin(4x)tan(5x) Find the limit. Use l’Hospital’s Rule where appropriate….**

Given the limit function limx→0sin(4x)tan(5x)limx→0sin(4x)tan(5x) . We have to find the limit. Applying the limit we can see that, limx→0sin(4x)tan(5x)=00limx→0sin(4x)tan(5x)=00 which is of the form 0000 . Hence we…

1 educator answer

**MATH**

**limx→(π2)cos(x)1−sin(x)limx→(π2)cos(x)1-sin(x) Find the limit. Use l’Hospital’s Rule where…**

You need to evaluate the limit, hence, you need to replace π2π2 for x such that: limx→π2cosx1−sinx=cos(π2)1−sin(π2)=01−1=00limx→π2cosx1-sinx=cos(π2)1-sin(π2)=01-1=00 Since the limit is…

1 educator answer

**MATH**

**limx→(12)6×2+5x−44×2+16x−9limx→(12)6×2+5x-44×2+16x-9 Find the limit. Use l’Hospital’s…**

limx→126×2+5x−44×2+16x−9limx→126×2+5x-44×2+16x-9 =limx→12(2x−1)(3x+4)(2x−1)(2x+9)=limx→12(2x-1)(3x+4)(2x-1)(2x+9) =limx→123x+42x+9=limx→123x+42x+9 plug in the value, =3⋅12+42⋅12+9=3⋅12+42⋅12+9 =3+82+18=1120=3+82+18=1120

1 educator answer

**MATH**

**limx→1×3−2×2+1×3−1limx→1×3-2×2+1×3-1 Find the limit. Use l’Hospital’s Rule where…**

limx→1×3−2×2+1×3−1limx→1×3-2×2+1×3-1 =limx→1(x−1)(x2−x−1)(x−1)(x2+x+1)=limx→1(x-1)(x2-x-1)(x-1)(x2+x+1) =limx→1×2−x−1×2+x+1=limx→1×2-x-1×2+x+1 plug in the value, =12−1−112+1+1=12-1-112+1+1 =-1/3

1 educator answer

**MATH**

**limx→2×2+x−6x−2limx→2×2+x-6x-2 Find the limit. Use l’Hospital’s Rule where…**

limx→2×2+x−6x−2limx→2×2+x-6x-2 =limx→2(x−2)(x+3)x−2=limx→2(x-2)(x+3)x-2 =limx→2(x+3)=limx→2(x+3) plug in the value, =(2+3) =5

1 educator answer

**MATH**

**limx→1×2−1×2−xlimx→1×2-1×2-x Find the limit. Use l’Hospital’s Rule where…**

limx→1×2−1×2−xlimx→1×2-1×2-x =limx→1(x+1)(x−1)x(x−1)=limx→1(x+1)(x-1)x(x-1) =limx→1x+1x=limx→1x+1x plug in the value, =1+11=1+11 =2

1 educator answer

**SCIENCE**

The transition metals are the metals that make up groups 3-12 of the periodic table. This region is called the d-block because it corresponds to the d electron sublevels filling. Some of the bettor…

1 educator answer

**LAW AND POLITICS**

**Name four differences between the U.S. Constitution and the Confederate States Constitution in…**

One of the main reasons why the Southern states seceded was that they wanted states to have more power (so they could have slavery). To make sure that the states had more power, they made a new…

1 educator answer

**HISTORY**

**Which were the two largest immigrant groups in the United States in 1914?**

The period of “New Immigrants” between 1885-1920 marked a shift in the type of people coming to the United States. Immigrants from this era were primarily from south and east Europe. Immigration…

1 educator answer

**THE GREAT GATSBY**

**“You are worth the whole goddamn rotten bunch” Discuss to what extent you would agree with Nick.**

Nick’s comment about Gatsby’s worth is an accurate one in that he actually earned all of his money, albeit through illegal means. “The bunch” Nick refers to here—Daisy and Tom—inherited their…

1 educator answer

**MARRIAGE IS A PRIVATE AFFAIR**

**What is the exposition in the short story “Marriage Is a Private Affair”?**

In a piece of literature, the exposition is the part of the story which introduces the important background information, including setting, characters and potential conflicts. In the first few…

1 educator answer

**A CHRISTMAS CAROL**

**In A Christmas Carol, which character in the novel was most influential on Scrooge in making him…**

Jacob Marley had the greatest effect on Scrooge, because he created the opportunity for his transformation. There was not just one character who had an influence on Scrooge. However, since Jacob…

1 educator answer

**THE OUTSIDERS**

**What opportunity is Kit given to earn “real wages”?**

Kit is excited when Mercy tells her that she has been recommended by Dr. Bulkeley to teach the young children in the dame school. Kit is recommended because she can read. Mercy has already been a…

1 educator answer

**SCIENCE**

**How does physical science explain most of what you do in your daily life?**

Physical science deals with non-living things and includes physics, chemistry, earth science, etc. Many aspects of our day to day can be explained by physical science. Here are some examples: The…

1 educator answer

**SCIENCE**

**Factor affecting rate of electrochemical corrosion?**

Electrochemical corrosion is a oxidation-reduction reaction in which electrons in a metal are transferred to an electron acceptor, resulting in oxidation of the metal. The electrons migrate through…

1 educator answer

**NIGHT**

**What are five examples of hopelessness and death and five examples of hope and life in chapters…**

Not surprisingly, there are several examples of hopelessness and death in the final four sections of Elie Wiesel’s memoir Night. The sections focus on the deportation from Buna, Elie’s father’s…

1 educator answer

**SOCIAL SCIENCES**

**With the aid of an appropriate diagram, analyze the effect of an increase in consumers’ income…**

If these two changes occur at the same time, we know that the equilibrium price will rise and the equilibrium quantity may drop or may rise. This is true because we will see an increase in demand…

1 educator answer

**HISTORY**

**Why did John Brown not achieve the goals he had set?**

John Brown failed to achieve his goal because his goal was not something that an individual citizen could possibly accomplish. Brown wanted to end slavery and that was something that could only be…

1 educator answer

**GREEK MYTHOLOGY**

**What would be a good thesis for an essay about the origin of Greek mythology and the Titans?**

There are two assumptions current in the study of the history of Greek mythology that could serve as starting points for a paper on the topic. The first might be stated as: “Walter Burkert has…

1 educator answer

**THE GREAT GATSBY**

**How does Jay Gatsby use Nick Carraway ?**

Many years prior to the setting of The Great Gatsby, Jay Gatsby fell in love with Daisy but was unable to secure them a stable life together. When he had to leave for the war, the two broke up and…

3 educator answers

**LITERATURE**

**What are some examples of voiced and unvoiced consonants?**

Consonants that are “voiced” are those whose sound comes from the vibration of the vocal cords. One way to tell is to put your fingers on your throat, and if you feel your larynx (voice box)…

1 educator answer

**THE MERCHANT OF VENICE**

**What is a brief character sketch of Bassanio as he is presented in The Merchant Of Venice? What…**

Bassanio plays a central role in the play. In fact, he is really the character who initiates the circumstances around which practically the entire play revolves. We learn that he is very close to…

1 educator answer

**OF MICE AND MEN**

**What do the themes fraternity and friendship mean in Of Mice and Men?**

If we break down the word, “Fraternity,” it comes from the Latin word, “Frater,” meaning “brother.” In the world of Of Mice and Men, fraternity and friendship are conspicuously missing, apart from…

1 educator answer

**THROUGH THE TUNNEL**

**How does Jerry’s experience help shape his identity?**

Jerry’s experience helps to shape his identity because his preparation and eventual ability to swim through the tunnel dramatizes his transition from a child to an adult. It starts with the “big…

1 educator answer

**HISTORY**

**Why did the invasion of the Angles, Saxons, and Jutes kill off the Celtic language, but the Roman…**

The best answer I can give you is that the Romans differed in their tactics for claiming Britain as compared to the Angles, Saxons, and Jutes. England was part of the Roman Empire from the year 43…

1 educator answer

**HISTORY**

The best answer to this is that we really simply do not know and almost surely never will know. Hitler was very guarded about his personal life so we do not know much about what really went on….

1 educator answer

**SCIENCE**

**The angle between an incident ray and a mirror is 60 degree. What is the total angle through…**

Hello! The incident ray, the normal and the reflected ray are lie in one plane, the law of reflection says. Also, angles between normal and incident ray, and between normal and reflected ray are…

1 educator answer

**FRANKENSTEIN**

**In what way is Elizabeth’s murder ironic or unexpected?**

To be fair, I think Elizabeth’s death is really only unexpected to Victor. After Victor destroyed the female he was creating at the request of the creature, the creature says, “‘I shall be with you…

1 educator answer

**TO KILL A MOCKINGBIRD**

**What are the main points in Heck Tate’s evidence? What does Atticus show in his cross-examination…**

Gilmer simply asks Heck basic questions. He wants the jury to hear what Mayella said when Heck got to the crime scene. She claims that Tom is the one who had hurt and taken advantage of her. This…

1 educator answer

**LORD OF THE FLIES**

**In the novel Lord of the Flies, what is the significance of the title of Chapter 2?**

Chapter 2 is titled “Fire on the Mountain.” The title of the chapter correlates with the significant event of the boys lighting their first fire on top of the mountain. In order to light the fire,…

1 educator answer

**THE GREAT GATSBY**

**What message do you think Fitzgerald was trying to convey to his reader about the relationships…**

The marriage between Tom and Daisy appears to be a marriage of convenience between two people of the same class. In the world of Gatsby, “old money” marries “old money.” It would be unacceptable…

1 educator answer

**THE ADVENTURES OF HUCKLEBERRY FINN**

**Which characters die in The Adventures of Huckleberry Finn? How do they die?**

There are several deaths throughout The Adventures of Huckleberry Finn. The first one would be the symbolic death of Huck. Huck fakes his death to get away from Pap and is metaphorically reborn on…

1 educator answer

**HISTORY**

People of the time would have had different views on John Brown’s actions depending on which side of the slavery issue they stood. To southerners, John Brown was a villain. He went into Kansas and…

1 educator answer