How to solve limit as x approaches negative infinity when there is a bigger x term in the denominator?

Posted by Timothy L. Wise

  1. “The limit as x approaches negative infinity of ( x – 2 ) / ( x squared + 1)

    I kind of get that this is suppose to be zero. That is the what the answer key says. I know that when talking about limits when dividing by infinity it is zero, and because the denominator is going to negative infinity faster (being x squared) than the x in the numerator, overall this is going to be zero, I guess. I just don’t know how to solve this all written out, like my math teacher wants me to write it out all, professionally, I don’t know. I just don’t know how to solve this written out mathematically without using words. How, please.

    Answer by Philip
    LHopital’s rule, for an indeterminate form, take the derivative of the numerator and denominator (separately) until a determinate form is obtained.
    lim x–>-infin (x-2)/(x^2+1) = lim x–>-infin 1/(2x) = 0

  2. X^2+2x+10
    I just need to know how to get an answer . I don’t need any bullshit websites (Kim). Please if anyone knows I’ll greatly appreciate it.

    Answer by KY
    The x-intercept is where the function crosses the x-axis, or when the function is equal to zero.

    x² + 2x + 10 has no x-intercepts since it never touches the x-axis.

    If you use the discriminant b²-4ac, you have (2)² – 4(1)(10) = 4 – 40 = -36; this implies that the quadratic has no real roots and therefore, never crosses the x-axis.

    ANSWER

    x² + 2x + 10 has no x-intercepts

  3. Take these two equations:
    y=x²
    and y= √x

    If you graph both of them, what is the relationship between the two graphs.

    Note: The x and y values for both equations are reversed, so when x =4 and y =16 for one equation, x=16 and y=4 for the other.
    But what does this tell me mathematically?

    Answer by Spoonrad
    y1 = x^2
    y2 = √x
    The relationship between the two graphs?

    Well y1 = x^2 = √x * √x * √x * √x = y2^4
    So y1 = y2 for any x that belongs to [0 ; +infinite]

    So the graphs of y1 and y2 are always proportional, the proportion being k = y2^3 because y1 = y2^3 * y2
    This means Cy1 crosses Cy2 at 0 and 1
    Cy1 is below Cy2 on ]0 ; 1[ because…
    y1 – y2 = x^2 – √x
    = (√x)^4 – √x
    = (√x)[(√x)^3 - 1]
    lim (x -> 0) √x = 0
    lim (x -> 0) (√x)^3 = 0 => lim √x)^3 – 1 = -1
    So lim (x -> 0) y1 – y2 = 0 negative
    This means y1 – y2 < 0 so Cy1 is below Cy2

    You must also calculate the limit of y1 - y2 when x -> 1 and most likely also see the variations / signs of y1 – y2 as well if you really want to demonstrate this…

    Cy1 is above Cy2 on ]1 ; +infinite[ because…
    Same work.

    I’m guessing they don’t want you to demonstrate but just give the position and relationship between the graphs as an observation… I think what I’ve told you works.

  4. How do i simplify and identify any x-values for this expression that is undefined “(4x+20)/(-5-x)” The answer is “(7(2x-3))/(3(x-2)); x≠2″ all i need to know is how to do it honestly. Thanks in advance.

    Answer by Holly
    Just take (4x+20)/(-5-x) and solve for x

    4x + 20
    x=20/4 or 5

    -5-x
    x=-5

    So your fraction is -5/5 or -1

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i know people have asked this before but it is just not making any sense to me. I have been doing plenty of research but no success or at least i am not getting it. Please explain why time suddenly slows down even if you are going so fast. for example, from the US to Austrailia, traveling at the speed of light (186,000 miles per second)can reach austrailia in a matter of seconds though when you get to Austrailia, its years in the future. Though to the person traveling, its only been a couple of seconds. Answer by Aspiring CookUnfortunately, a really accurate description of the reason that time slows down at speeds close to that of light is beyond the scope of this forum. However, perhaps the following (very brief) account will suffice, with links to sites that may help much more. As an objects velocitys object approaches very close to the speed of light, that objects rate of time will slow down as observed by others moving slower in relation to the fast object. This effect is called time dilation. The effect occurs even at Keep On Digesting

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Understand this – Deciding On Buying Or Renting Commercial Property

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Write an easy-to-understand letter of intent, focusing on the biggest issues. You can worry about the little things later on. By coming to agreement on the larger issues, it will make the negotiations go much easier. Think about the ancient art of feng shui when it comes to your personal office and all of your commercial real estate properties. Two of the most basic principles of feng shui- open spaces and clutter-free lifestyles -are also very appealing to buyers.Creating your own real estate blog can help to establish you as an expert in the field. This helps to attract potential buyers if you have something for sale or lease.Keep watch for sellers who are looking to get rid of their properties quickly. You will have to actively find them, especially those who are motivated enough to sell the property below the market value. You will achieve nothing in commercial real estate unless you get your hands on a good deal, and that most often will happen as a result of an offer made by an eager seller.If you are new to commercial real estate Keep On Digesting

Beat The Hosepipe Ban

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Hosepipe ban news... No matter how we may all feel about it, the reality is many people will be experiencing one of the current hosepipe bans which most suppliers expect to last all Summer, perhaps into Autumn and beyond. The BBC reported that it will effect about 20 million people and those who flout it could fined up to 1,000. Even if you are not affected we should all be smarter about how we use water. With a couple of simple measures and innovative products you can save water and your money. Find out how below. This very clever & effective design allows you to clean your Car, Windows, Conservatory, Boat, Caravan etc using very little water. Not only will you be able to effectively clean everything you used to clean with your hosepipe during the ban, but you will be helping the environment. Doing that your wallet by not getting a 1000 fine due to the hosepipe ban! Not just for use during a ban! You will use less water with this system which means you will also have less waste and if you have a water meter less water used means Keep On Digesting

Understand this – Don’t Wait: Use These Tips To Help You Make The Right Life Insurance Decision Today

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If you have no dependents, such as children, spouses or life partners, there is a good chance that you do not need life insurance at all. Life insurance is designed to protect your dependents from financial hardship in the event of your death. If you don't have dependents and don't intend to have children, then you don't really need to spend the money to get life insurance.Never reveal too much of your personal information when you are shopping for insurance quotes online. Many scammers claim to be offering life insurance, but really just want your information to steal your identity. Try to remember that the only initial info you should need to give for a quote is a zip code. To save money on your life insurance policy and insure that you have made the best decision, purchase your policy from a company that is financially solid. There are independent agencies that will research and grade insurance companies. Look for an A rating or higher from these companies. Before purchasing a life insurance policy, you must always perform research on Keep On Digesting

flirt

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Few Interesting flirt Pix

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    Image by jenny downing
    (desaturated very slightly as I mussed up the camera settings and the highlights were blown)

  2. Flirt

    Support This Blog By Visiting Sponsor Blog pertaining to Paddy Power -
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    Image by Daniele Pesaresi
    People passing by, flirting anf taking photos under one of Pragues bridge