Thread: isoclines,,,never been very good with limits

can u cancel infinty,,,,this is probably a very stupid/petty question!!Q is find the equation of the straight line on which the gradient of the solution curve is infinite. I made the presumption that this straight line would essentially be an isocline(hopefulli im ryt) and did the follwing,, Is is more accurate using the D.e and making bottom=0???Or is my working ok?!

dy/dx=(3y-x)/(y+x)

dy/dx=m(constant)

putting constant as infinity and rearranging to f(x)

(i) y= -x(1-m)/(m-3)
(ii) y= -x(1-inf)/(inf-3) implies(i think) y= -x(inf)/(inf)
y = -x

is this okai???

Originally Posted by i_zz_y_ill

can u cancel infinty,,,,this is probably a very stupid/petty question!!Q is find the equation of the straight line on which the gradient of the solution curve is infinite. I made the presumption that this straight line would essentially be an isocline(hopefulli im ryt) and did the follwing,, Is is more accurate using the D.e and making bottom=0???Or is my working ok?!

dy/dx=(3y-x)/(y+x)

dy/dx=m(constant)

putting constant as infinity and rearranging to f(x)

(i) y= -x(1-m)/(m-3)
(ii) y= -x(1-inf)/(inf-3) implies(i think) y= -x(inf)/(inf)
y = -x

is this okai???

If your question is



Then we would have as you observed



giving us



EDIT: Please, for your sake never make this connection




Counter example



But

nah i think the m value should just equal infinty. If you imagine all the direction indicators on a tangent field being vertical in which case i believe there'll be no limits excuse my wording earlier. Erm my query was more in this situation by putting m = inf does this diminish the accuracy of my working when i say that y= -x(1+inf)/(inf - 3) is the equivalent of y= -x(inf/inf) in which case inf would cancel leaving me witht the right answer x + y = 0




oh ryt:P errrr well isnt it f(x)/f(x) where the bottom is only a constnt so im not reli doing that. Iim still confsed as to whether i should use limits or not?? lol i should just equate the bottom to zero

Originally Posted by i_zz_y_ill

nah i think the m value should just equal infinty. If you imagine all the direction indicators on a tangent field being vertical in which case i believe there'll be no limits excuse my wording earlier. Erm my query was more in this situation by putting m = inf does this diminish the accuracy of my working when i say that y= -x(1+inf)/(inf - 3) is the equivalent of y= -x(inf/inf) in which case inf would cancel leaving me witht the right answer x + y = 0

It is very hard to understand what you are saying. But if you are asking can you just say that since m tends towards infinity that the quotient of the m terms is -1, yes. But if you will look above cancelling infinities is a mathematically unforgivable act

k cheers i think i can see where im wrong now(didtn read q), i'll ook out for that error aswell !!!thnx