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anonymous
 5 years ago
I am trying to sketch the curve y=x+1/x
Following are the steps that are generally followed. But I don’t understand one thing
First I note that while as x tends to infinity, 1/x tends to 0. Then we conclude that y tends x, since 1/x tends to 0. The thing that I don’t understand is if x tends to infinity, so why don't we say y tends to infinity too.
anonymous
 5 years ago
I am trying to sketch the curve y=x+1/x Following are the steps that are generally followed. But I don’t understand one thing First I note that while as x tends to infinity, 1/x tends to 0. Then we conclude that y tends x, since 1/x tends to 0. The thing that I don’t understand is if x tends to infinity, so why don't we say y tends to infinity too.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0y = (x+1)/x ? or y = x + (1/x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I mean using the math rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First division then addition...................

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0id say its y = inf + 0 as well...... is there an answer that says differently?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Its curve sketching. If I say that way, the curve turns out to be wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0iamignorant, Is the following your expression? \[y=x+\frac{1}{x} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[y==1+\frac{1}{x} \] The 2 attached plots should help visualize the function. The first plot is from x=10 to +10. The scale of the plot is too large and should be reduced in your pdf viewer. The second is from x= 4000 to x= +4000. To the the casual observer the plot looks like a straight line drawn through the origin and making an angle of Pi/4 with the x axis.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just reviewed what was put on the net. The plots seem to be OK.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You see the problem that is disturbing me is a little different

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am trying to sketch the curve using the asymptote location method

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And I have presented the problem that I face while reasoning

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I understand that while 1/x tends to infinity y must tend to x, or else y=x will not be an asymptote

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But I don't understand where exactly I misreasoned to make it otherwise

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0y = (x^2 +1)/x is an equivalent equation right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then the asymptote is a slant/oblique right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, but how did you conclude that?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the ends approach y=x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hold on a few minutes. I want to set up some Limits.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the top is one degree highr than the bottom

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually I am not aware of that rule

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when we divide it all by x we get: x +1/x  1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0anyting with an x on the bottom goes to zero; which leaves us with y = x as the slant asymptote

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You mean when 1/x tends to zero anyting with an x on the bottom goes to zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is that what you mean?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so you have 2 curves that trail in the ends to the line y=x; and in the middle skirt along the x=0 axis: like this

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good job amistre64. I have to break off. Thank you.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when the bottom of a fraction gets large; the value gets small: 1  = .000000...00001 1000000...0000

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so anything with an x on the bottom; as the x gets large; the value goes to zero.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0whats left over is what your asymptote is :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, when x is tending towards infinity 1/x tends to zero (this is what you say), but x is tending to infinity so y=x+0 means y is tending to infinity. This is what I don't understand

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0y is keeps going up and skirting next to the y=x line; instead of a y=3 line, its the y=x line. that line has a range of (inf,inf)
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