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swin2013
 2 years ago
Limit problem?
swin2013
 2 years ago
Limit problem?

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swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow 3^{+}} 1/x+3\]

across
 2 years ago
Best ResponseYou've already chosen the best response.1You have that\[\lim_{x\to3^+}\frac1{x+3}.\]Immediate substitution yields a division by zero. Therefore, you must have a vertical asymptote there. Approaching it from the right side, however, will yield \(\infty\) as the limit. On the other hand, approaching it from the left side will yield \(\infty\) as the limit.

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.1i am soory i read it wrong

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1since it is on the right side, do i write that the limit is approaching positive infinity?

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.1actually the limit DNE because the absolute value get very large

across
 2 years ago
Best ResponseYou've already chosen the best response.1Because it's a sided limit, you have to specify \(\text{where}\) it goes. Simply writing DNE won't suffice.

viniterranova
 2 years ago
Best ResponseYou've already chosen the best response.0I got it 1/6. Just plug it into the equation

across
 2 years ago
Best ResponseYou've already chosen the best response.1@viniterranova, how did you get \(1/6\)?

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1I'm pretty sure i should get either  infinity or positive. I'm kind of unclear on what to write. I understand that when i divide the constant (1) by x2 (which is a small positive number), does that mean it's approaching positive infinity since 1 / x2 is getting positively bigger?

viniterranova
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=limit+x%3E+3%2B+%281%2F%28x%2B3%29

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1@viniterranova it's actually negative 3. it appears that the equation plugged in 3. if we plug in the value of 3, we get 0 on the denominator which is not valid since the denominator can't be zero

across
 2 years ago
Best ResponseYou've already chosen the best response.1@swin2013, when you're asked to compute\[\lim_{x\to3^+}\frac1{x+3},\]if you substitute the limit, \(3\), you'll have that\[\frac1{x+3}=\frac1{(3)+3}=\frac10.\]Therefore, you know that the limit DNE. However, if you approach \(3\) from the right side, you'll have that\[\frac1{x+3}\]gets infinitely larger (since you're dividing by a really small number) toward \(\infty\). Oh, and @viniterranova, the limit is \(3\), not \(3\). Read the question again.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1so am i correct in the sense that x  infinity?

viniterranova
 2 years ago
Best ResponseYou've already chosen the best response.0See teh wolfram site.

viniterranova
 2 years ago
Best ResponseYou've already chosen the best response.0The fact of you have the minus sign after 3 doesn´t mean that the 3 is negative. Just mean that you are approaching from left.

across
 2 years ago
Best ResponseYou've already chosen the best response.1No, you silly, \(3\) is different from \(3^\).

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1no. if it's approaching 3 to the left, there will be a negative as an exponent

across
 2 years ago
Best ResponseYou've already chosen the best response.1@swin2013, for example, let \(k=2.99999\) be that close to \(3\). Then\[\frac1{k+3}=\frac1{2.99999+3}=\frac1{0.00001}=100,000.\]So you indeed approach \(\infty\).

across
 2 years ago
Best ResponseYou've already chosen the best response.1(Notice that we're close to it from the right side.)

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1thank you @across, i just need clarity on what to write for my answer haha. I already understand the concept :)

viniterranova
 2 years ago
Best ResponseYou've already chosen the best response.0Across you didn´t understand me. I just said minus sign after 3 not before.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1yea but the equation never stated a negative sign after the 3.

across
 2 years ago
Best ResponseYou've already chosen the best response.1That doesn't change the fact that you screwed up, @viniterranova. ;) @swin2013, you can write: "The limit does not exist as it approaches positive infinity."

across
 2 years ago
Best ResponseYou've already chosen the best response.1You can also just write\[\lim_{x\to3^+}\frac1{x+3}=\infty.\]It depends on your teacher.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1x  infinity no finite lim :)

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.1the correct way to say according to textbook is it DNE

across
 2 years ago
Best ResponseYou've already chosen the best response.1lol @ksaimouli, you are right, but this is a SIDED LIMIT. In other words, YOU MUST SPECIFY WHERE IT IS GOING. <:)

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1lol i never said INFINITE i said FINITE

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1which is the same as DNE as in there is not possible limit

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.1or DEFINITE limit (the derivative of FINITE)
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