Finding the limit of a function

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To find the limit of the function lim (x-1)/(1-x) as x approaches negative infinity, the constants 1 and -1 become negligible. The function simplifies to x/-x, which equals -1. Therefore, the limit is confirmed to be -1. The key takeaway is that when evaluating limits at infinity, constant terms can often be disregarded. The final answer for the limit is -1.
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Homework Statement



lim x-1/1-x
x-->-infinity



Homework Equations



none really



The Attempt at a Solution



Other questions relating to this part of limits have us factor out the x from the function. So when I take the x out of the function I get 1/-1 with a final answer of -1.

Is this correct?
 
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You don't "take x out of the function." You note that the constant 1 and -1 are not relevant when x is very large. The equation reduced to x/-x = -1. There's your limit.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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