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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2 Strategies – Fantastic Fitness Ideas You Can Put To Good Use

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Building tougher abdominal muscles is a great way to maximize the efforts you are making to obtain better fitness. You can achieve this by doing morning sit-ups with weights or not. Abs compose your body's core and can help make you more flexible. This can make your weight lifting more successful. Many people attempt to achieve physical fitness at the gym by lifting weights. If you want to improve your fitness, you only really need six simple exercises to work out all of your muscles. These exercises are pull ups, leg raises, bridges, handstand push ups, regular push ups, and squats. When doing situps or crunches, keep your tongue firmly pressed against your palate. Using this tongue position means that the muscles of your neck are involved in the exercise, keeping your head aligned while you move. This way you avoid harmful strains and accidental injury. You might like a treadmill, but running in the outdoors is better for you. Treadmills are convenient, but nature (with a little help from man) has created the perfect workout just outside Keep On Digesting

Create Your Cash From Kitchen With A Home Business

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When running a home business be sure to schedule specific business hours. It can be extremely difficult when you start a home business to stay out of the office, but if you want to keep your sanity and maintain a positive relationship with others you want to be sure to make time for each, and set a standard that others can expect from you. Back up important documents pertaining to your business with removable storage. The result would be losses in the thousands and having great difficulty when it comes to accurately filing taxes. Another backup option is to use online backup solutions like Mozy. Go on a business trip. Business trips, unlike vacations, are at least partially deductible from your taxes. You can take a vacation and business trip in one if you are lucky enough to find a valuable business conference in your niche that is also located in a great tourist destination. This can help you deduct the trip legally and remain safe from the IRS.You should record all business expenses in order to save money. Make sure to include smaller Keep On Digesting

One might want to fully grasp – Everything You Ought To Know About Cell Phones

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Don't text while you are driving. While you may be tempted to quickly send out a text, this is not safe. Instead, wait until you are at your destination and vehicle is stopped. This assures that you are giving your full attention to the road while you are driving. Utilize the voice to text feature on your phone to save time and be safe on the road. This will allow you to convert the words that you say to a text message instantaneously. If you do not have this feature on your smartphone, you can add software like ReQall which will employ it.Keep an eye out for extended warranties. Generally, these added costs are nothing more than that. You will notice most problems within the first year generally, and the original warranty covers any of those issues. Many people also purchase a new phone yearly; these people do not need an extended warranty.A screen protector may not be necessary. The latest screens generally have a protective layer already included. A screen protector may make it difficult for you to see your screen or even make it harder Keep On Digesting

Techniques To Creating Your Home Based Business Successful

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Make sure that your lunch breaks include laughter! Laughing will rejuvenate your mind and make you ready to return to work. Find humorous videos on YouTube, and then prepare to dive into your work again after you have had a good giggle. Make sure you keep your messages to your clients at a reasonable level so that you give them the information they need to know but do not overload them. Offer email alerts or newsletters, especially if you have frequent discounts or your website is updated often. Be sure that you only contact your customer as much as they request from you. Make yourself accessible by email, telephone or regular mail. Keep up with your contacts. Find out what purchases they made by asking plenty of questions. Its possible that the information or answers that you provided caused them to want to buy your product. Speak with them and find out what helped them come to their decision. When your product is out of stock, be sure to say so. Its very upsetting to order an item and then find out that the shipment will take weeks or Keep On Digesting