LIMITS approaches o+ - how come?

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In summary: Well, if an equation has a v in it, then the limit is infinity. So the answer to the question is always infinity.
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noobie!
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LIMITS approaches o+ - how come??

i encountered a few ques which makes me baffle whn i stdy about infinite limit.. as we know limit x --->0+ it will be positive infinity and when x-->o- it will be negative infinity; first of all m i rite?then..a que which i encountered was lim x --->-8+ (2x/ x+8) homework cum i get negative infinity instead of positive infinity?it makes me so confuse..so could any1 please rectify my mistakes for those theorem?please?! thanks a lot 1st..:confused:
 
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Well, what sign will a fraction between two negative numbers have? A negative sign, or a positive sign?
 
  • #3


arildno said:
Well, what sign will a fraction between two negative numbers have? A negative sign, or a positive sign?

huh,umm i don't really get what u mean;but isit negative?:confused:
 
  • #4


Intuitively, [tex]\lim_{x \to -8^+} 2x/(x+8)[/tex] is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
 
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  • #5


adriank said:
Intuitively, [tex]\lim_{x \to -8^+} 2x/(x+8)[/tex] is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
[/URL]

thanks alot..rite nw i have no doubts..thanks for your kind help..thanks..:wink:
 
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  • #6


adriank said:
Intuitively, [tex]\lim_{x \to -8^+} 2x/(x+8)[/tex] is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
[/URL]

one more doubt is let say an example: [(1/x^1/3) - (1/(x-1)^4/3 ] ;its limit is x --->0+ and 0- so the answer will be positive infinity because of v sub x=o into the equation ,thus its infinity minus 3 that's why we got positive infinity same goes to 0- ?please rectify my mistakes if i have thm..thanks :blushing:
 
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FAQ: LIMITS approaches o+ - how come?

What is a limit and how does it approach infinity?

A limit is a mathematical concept that represents the value that a function or sequence approaches as its input or index approaches a certain value. When a limit approaches infinity, it means that the function or sequence increases without bound and has no finite limit.

Can a limit approach both positive and negative infinity?

Yes, a limit can approach both positive and negative infinity. This means that the function or sequence has different behaviors as the input or index approaches different values.

How can we determine the limit of a function or sequence approaching infinity?

To determine the limit of a function or sequence approaching infinity, we can use various mathematical techniques such as the squeeze theorem, L'Hôpital's rule, and the comparison test. These methods help us to simplify the function or sequence and evaluate its behavior as the input or index approaches infinity.

Are there any real-life applications of limits approaching infinity?

Yes, there are many real-life applications of limits approaching infinity, such as in physics, economics, and engineering. For example, in physics, limits approaching infinity are used to calculate the velocity of an object at a certain time as it approaches infinite time.

What are the common misconceptions about limits approaching infinity?

One common misconception about limits approaching infinity is that it represents the actual value of the function or sequence at infinity. In reality, a limit only indicates the behavior of the function or sequence as it approaches infinity, not the actual value at infinity. Another misconception is that limits approaching infinity always result in infinity, but this is not always the case as the limit may approach a finite value.

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