FrostedMango
New member
- Joined
- Sep 2, 2007
- Messages
- 3
First Problem: Can the graph of y = f(x) intersect a vertical asmptote? Can it intersect a horizontal asymptote? How many asymptotes can the graph of y = f(x) have? Sketch.
The part I didn't understand was y = f(x), wouldn't this simply be saying y = y, well that's how I thought it and which in that case, the graph isn't exactly a graph anymore... so can someone help me to understand what y = f(x) is suppose to mean?
Second problem: Find lim [x -> infinity] cos(x)
the part i was confused at was that as "x" approaches infinite, the graph just keeps on going up and down between y = 1 and -1. So does that mean there is no limit or if so, how do we illustrate a limit where there are two of them?
Third problem: A tank contains 5000L of pure water. Brine that contains 30g of salt per liter of water is pumped into the tank at a rate of 25L/min. Show that the concentration of salt after t minutes (in grams per liter) is: C(t) = 30t/(200+t)
The part I'm confused at was... well pretty much the question itself. It told me to show that the equation is correct (i think), but I didn't understand the quesoitn at all. So is it asking if that equation is right and prove it by just plugging in random values into it or waht is it asking?
Fourth problem: Find lim [x -> -infinity] sqrt(x^2 + x + 1) + x
ok, so I tried it out and I got a wrong answer, i ended up with DNE, can you tell me where I went wrong if you can? so this is what i did: (by the way, the question actually was in 3 parts, first 2 which of finding the limit and third, which is what I'm doing now is to prove it)
1. (sqrt(x^2 + x + 1) + x) * (sqrt(x^2 + x + 1) - x)/(sqrt(x^2 + x + 1) - x)
2. (x + 1) / (sqrt(x^2 + x + 1) - x)
3. (x/x + 1/x) / (-sqrt(x^2 + x + 1)/sqrt(x^2)) - x/x
4. (1 + 1/x) / -sqrt(1 + 1/x + 1/x^2) - 1
Since x is to negative infinite, 1/x, 1/x^2 become insignificant, so I considered them to be 0
5. -1 / sqrt(1) - 1
6. -1 / 1 - 1 = -1 / 0 = DNE
The part I didn't understand was y = f(x), wouldn't this simply be saying y = y, well that's how I thought it and which in that case, the graph isn't exactly a graph anymore... so can someone help me to understand what y = f(x) is suppose to mean?
Second problem: Find lim [x -> infinity] cos(x)
the part i was confused at was that as "x" approaches infinite, the graph just keeps on going up and down between y = 1 and -1. So does that mean there is no limit or if so, how do we illustrate a limit where there are two of them?
Third problem: A tank contains 5000L of pure water. Brine that contains 30g of salt per liter of water is pumped into the tank at a rate of 25L/min. Show that the concentration of salt after t minutes (in grams per liter) is: C(t) = 30t/(200+t)
The part I'm confused at was... well pretty much the question itself. It told me to show that the equation is correct (i think), but I didn't understand the quesoitn at all. So is it asking if that equation is right and prove it by just plugging in random values into it or waht is it asking?
Fourth problem: Find lim [x -> -infinity] sqrt(x^2 + x + 1) + x
ok, so I tried it out and I got a wrong answer, i ended up with DNE, can you tell me where I went wrong if you can? so this is what i did: (by the way, the question actually was in 3 parts, first 2 which of finding the limit and third, which is what I'm doing now is to prove it)
1. (sqrt(x^2 + x + 1) + x) * (sqrt(x^2 + x + 1) - x)/(sqrt(x^2 + x + 1) - x)
2. (x + 1) / (sqrt(x^2 + x + 1) - x)
3. (x/x + 1/x) / (-sqrt(x^2 + x + 1)/sqrt(x^2)) - x/x
4. (1 + 1/x) / -sqrt(1 + 1/x + 1/x^2) - 1
Since x is to negative infinite, 1/x, 1/x^2 become insignificant, so I considered them to be 0
5. -1 / sqrt(1) - 1
6. -1 / 1 - 1 = -1 / 0 = DNE