Understanding Limits: Evaluating lim x->∞ and lim x->-27 for 2 Questions

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In summary, for question 1, the limit as x approaches infinity will approach 0 because the highest degree of the numerator and denominator are the same. For question 2, the limit as x approaches -27 will equal the value of the function, which is 0.
  • #1
kiss89
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I have 2 questions about limits :

1)Evaluate : lim as x approaches infinity for
(3x-4-4x^2) / (x^2 -16)

2)Evaluate: lim as x approaches -27 for
(27+x) / ( 7/2 + 3 )

thank u.
 
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  • #2
kiss89 said:
I have 2 questions about limits :

1)Evaluate : lim as x approaches infinity for
(3x-4-4x^2) / (x^2 -16)

2)Evaluate: lim as x approaches -27 for
(27+x) / ( 7/2 + 3 )

thank u.

If you show us some work, we will be glad to help you.
 
  • #3
Sorry about that...heres my work
http://img88.imageshack.us/img88/9971/img002sy9.png
 
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  • #4
kiss89 said:
I have 2 questions about limits :

1)Evaluate : lim as x approaches infinity for
(3x-4-4x^2) / (x^2 -16)

2)Evaluate: lim as x approaches -27 for
(27+x) / ( 7/2 + 3 )

thank u.

for #1, in order to find the limit as x approaches infinity you need to divide the numerator/denominator by the highest power of x in the denominator, in this problem it would be x^2.
Doing this you'd end up with some 1/x's or x^n times some constant (1,2,3,...) which =0 when you take their limit as x approaches infinity

for #2, lim as x approaches a for f(x) = f(a) IF a is in the domain of f
 
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  • #5
For #2, when you plug -27 in you get a number over a nonzero. That means the limit equals the value of the function, in this case, 0
 
  • #6
what about Q.1 i still don't understand how to solve it using infinity?
 
  • #7
In the limit, only the highest degree matters. Because the numerator and denominator have the same degree, the function will have a limit (horizontal asymtote) approaching infinity. Divide the coefficient of the numerator by the coefficient of the denominator and you have all that's left when x is big. Your post is different from your work, but either way the answer should be apparent in 2 seconds
 

What is a limit?

A limit is a fundamental concept in mathematics that describes the behavior of a function as its input approaches a certain value. It represents the value that the function is getting closer and closer to, but may not necessarily reach.

Why are limits important?

Limits are important because they allow us to analyze the behavior of a function at points where it may not be defined or where it is difficult to evaluate. They also help us understand the continuity and differentiability of a function.

How do you find the limit of a function?

To find the limit of a function at a specific point, you can plug in values that approach that point from both sides and observe the behavior of the function. You can also use algebraic manipulation or graphing techniques to determine the limit.

What are the different types of limits?

The different types of limits include one-sided limits, where the function is evaluated from only one side of the point, and two-sided limits, where the function is evaluated from both sides of the point. Other types of limits include infinite limits and limits at infinity.

What is the relationship between limits and continuity?

Limits and continuity are closely related concepts. A function is continuous at a point if the limit of the function at that point exists and is equal to the value of the function at that point. In other words, for a function to be continuous, its limit must exist and be equal to the function's value at that point.

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