Limit as x approaches negative infinity

In summary, the limit as x approaches negative infinity is a mathematical concept that represents the value that a function approaches as the input (x) gets closer and closer to negative infinity. It is calculated by evaluating the function at values of x that are closer and closer to negative infinity. The limit can be undefined if the function has a vertical asymptote or oscillates at negative infinity. Its significance lies in understanding the behavior of a function and finding its horizontal asymptote. In real-world applications, it can be used in various fields such as physics, engineering, and finance to model long-term trends and behaviors.
  • #1
hangainlover
83
0

Homework Statement



as x approaches negative infinity, what value does this function approach ?

limit square root (X^2+X) + X






Homework Equations





The Attempt at a Solution


First, i manipulated the given function to take out absolute (x) from the square root



so, what i get is, limit absolute value (x) square root (1+1/x) +x



now, i get infinity - infinity. (looks like an indeterminate form)

I do not know where to go from this point.



Thanks
 
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  • #2
Pull the x down into the denominator, then use L'Hopital's rule.
 

FAQ: Limit as x approaches negative infinity

What is the definition of "Limit as x approaches negative infinity"?

The limit as x approaches negative infinity is a mathematical concept that represents the value that a function approaches as the input (x) gets closer and closer to negative infinity, which is the negative version of infinity.

How is the limit as x approaches negative infinity calculated?

The limit as x approaches negative infinity is calculated by evaluating the function at values of x that are closer and closer to negative infinity. If the values of the function approach a specific number as x gets closer to negative infinity, then that number is the limit.

Can the limit as x approaches negative infinity be undefined?

Yes, it is possible for the limit as x approaches negative infinity to be undefined. This can happen if the function has a vertical asymptote at negative infinity or if the function oscillates between different values as x gets closer to negative infinity.

What is the significance of the limit as x approaches negative infinity?

The limit as x approaches negative infinity is important because it helps us understand the behavior of a function as the input approaches negative infinity. It can also be used to find the horizontal asymptote of a function, which is a line that the function approaches as x gets closer to positive or negative infinity.

How can the limit as x approaches negative infinity be used in real-world applications?

The limit as x approaches negative infinity can be used in various real-world applications, such as in physics and engineering, to model the behavior of a system as time or another variable approaches negative infinity. It can also be used in financial and economic models to analyze long-term trends and behaviors.

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