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Who is density-depedent and density-independent limitin factors in rosemountmn?
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Most limitin nutrient in agriculture?
dengue agent host environment
How does a limiting reagent affect how much product is formed?
The amount of product will be limited by the number of moles of the limitin... reagent.
How does limiting reagent affect how much product is formed?
The amount of product will be limited by the number of moles of the limitin... reagent.
What does epsilon represent in math?
In mathematics (in particular calculus), an arbitrarily small positive quantity is commonly denoted ε; see (ε, δ)-definition of limitIn mathematics, Hilbert introduced epsilon terms as an extension to first order logic; see epsilon calculus.In mathematics, the Levi-Civita symbol.In mathematics, to represent the dual numbers: a + bε, with ε2 = 0 and ε ≠ 0.In mathematics, sometimes used to denote the Heaviside step function.
Why is large heavy exoskeleton less limitin for arthropods that live in water?
Why is a large heavy exoskeleton less limiting for arthropods that live in the water?that is not the answer!!
What is a limit.... I referred many books and websites for this answer but i am unable to get it. Whatever may be the level i want you to make me understand this ones answer?
So this is going to be a rather drawn out explanation, but this is perhaps the first coherently-worded question I've seen on here in a while, so I'm going to take time to make sure I explain it comprehensively.In a basic sense, a limit is the dependent value that a function is approaching as it nears some value of the independent variable. This holds true for all dimensions of calculus (one-dimensional up to n-dimensional), but since you are asking this question, I will assume you are most familiar with two-dimensional calculus (y=f(x)). So, in more visual terms, the limit of a function is the y-value that the function approaches as its x-values nears a defined x-value on the x-axis. For a definite example, consider the following:f(x)=6x2+5 (also can be written as y=6x2+5)If you wanted to find the limit as x approached 3 for f(x), you would simply find the y-value that results from plugging in x=3 into the function. Thus, the limit as x approaches 3 of that function is f(3)=6*9+5=59. As x approaches 3, y approaches 59. This is a very basic limit, though, and is of the type that you will rarely see in high school or collegiate math past a basic introduction to limits. What is of more interest in these classes as you progress onward is what happens when a function does not exist or is discontinuous at the value of x in question.First, some syntax issues must be addressed. I cannot create an image of a proper limit on this limited text-editing applet, so I have copied an image from Wikipedia [EDIT: These are not showing up in my broswer, they might in other browsers (I use IE). Simply go to http://en.wikipedia.org/wiki/Limit_of_a_function and look under the "Definitions" heading to see this image and the two I am refer to later on].The "lim" part of the syntax simply means "take the limit of""x-->p", which reads as "as x approaches p" denotes what value of x will be investigated"f(x)" is simply the function to be explored"L" is the numerical value that will result from the limitIn whole, this reads as "The limit as x approaches p of f(x) is L"This particular type of limit is what is known as a general limit, meaning that as x approaches p from both sides, the function equals the same value. Since you can either approach p from values less than p or from values greater than p on the x-axis, the limit can change depending on what side the x-value is approached from. For a general limit to exist, the limit must be the same regardless of approach direction.One-sided limits are limits that specify which direction the x-value is being approached from. Some generalized examples:(I)(II)Figure I is a limit as x is approached from the right, from x-values greater than pFigure II is a limit as x is approached from the left, from x-values less than p.For a general limit to exist, these two limits must equal each other.For our earlier example equation f(x)=6x2-5, the general limit as x approaches 3 exists because the limits as x approaches 3 from both the left and the right equal the same value. To see this, perform simple calculations:As x approaches 3 from the right (values greater than 3):f(10)=595f(5)=145f(4)=91f(3.5)=68.500f(3.1)=52.660f(3.05)=50.815f(3.01)=49.361f(3.001)=49.036As the values get infinitesimally closer to 3 (but never equalling 3), the resultant y-values get extremely close (but never equalling) to 49. From this, is is evident that the limit of f(x) as x approaches 3 from the right is 49.As x approaches 3 from the left:f(0)=-5f(1)=1f(2)=19f(2.5)=32.500f(2.9)=45.460f(2.99)=48.641f(2.999)=48.964As x gets closer and closer to 3, y gets ever closer to 49. From this, it is evident that the limit of f(x) as x approaches 3 from the left is 49.Since the limits from left and right equal each other, it can be said that a general limit as x approaches 3 of f(x) is 49.This particular method of determining limits does not always work, and it is heavily dependent on the continuity of the function as that certain point in question. If the function is continuous, you can easily employ the above method to find the limits from both sides. If it is continuous, you can even skip those steps and simply substitute the x-value in question directly into the equation to find its general limit.However, it is very important to note that if the function is not continuous at the point in question, simple direct substitution cannot be employed.As I said before, what is usually the most in question is the limit of a function when it the function approaches a discontinuity. Consider the function y=1/x. If you cannot visualize it in your head, use a graphing calculator or input the command "plot y=1/x" into Wolfram|Alpha (www.wolframalpha.com). This function has a discontinuity at x=0 because inputting x=0 into the equation would call for division by zero, which is impossible. This type of discontinuity is an asymptote, because the values diverge upward or downward as the x-values near the value where the function does not exist. This will differ from later types of discontinuties. As you can see, as the x values approach zero from the left, the y-values begin to steeply decrease in a seemingly infinite fashion. Similarly, as the x-values approach zero from the right, the y-values seem to increase steeply in an infinite fashion. This, as it turns out, is true. The values approach infinity as x approaches zero. Whether it is negative or positive infinity depends on the direction of approach. To examine this, employ the same subsitution method as before. As x approaches zero from the right:f(1)=1f(.5)=2f(.1)=10f(.05)=20f(.01)=100f(.001)=1000These values, as is apparent, keep increasing, and at an increasing rate of change. The values will keep increasing as the x-values get closer to zero. There are an infinite number of smaller decimal values between x=0 and x=1, so you can continue this forever, but never reach x=0, and the y-values will keep increasing forever as well. Therefore, the limit of f(x) as x approaches 0 from the right side is positive infinity. A similar method can be applied to the limit from the left, and it will be found to be negative infinity.Let us examine a different type of discontinuity: the jump discontinuity. At this type of discontinuity (see this image: http://learn.uci.edu/media/OC01/11113/AR0111001_L03T13P01.jpg) the limit from the left is a definite number (not an infinity), and the limit from the right is a definite number, but these two numbers are not equal. As is apparent from looking at the image of the graph, the limit of this function as x approaches 0 from the right is -3, but from the left it is 2. Going back to our definition of a general limit, we must therefore conclude that no general limit exists for this function as x approaches 0. However, we can state its two one-sided limits if asked for.A third type of discontinuity is not necessarily a traditional "discontinuity" in the traditional mathematical parlance, but it does come into play when evaluating general limits (and it is a tricky problem that calculus teachers and AP tests like to use). Consider the function y=ln(x). Again, type "plot y=ln(x)" into Wolfram|Alpha if you must. A property of all logarithmic functions is that they do not exist for negative numbers or zero. ln(x) is simply a special logarithmic function, so it does not exist for negative numbers or zero either. As you approach x=0 from the right side, the y-values approach negative infinity. It is impossible to approach from the left side, since no values exist to the left of x=0 on the function. So, since no left-side limit exists, there is no left-side limit value to compare the right-side limit value to, so there is automatically no general limit of this function as x approaches 0.The final type of discontinuity is referred to as a "hole" discontinuity. This type of discontinuity occurs when a functions seems perfectly continuous except for one exact x-value, which makes a "hole" in the function where no y-value exists. This usually occurs in functions that are comprised of a function divided by another function, where the denominator and numerator functions (on bottom and top) could possibly equal zero (which would imply the indeterminate form 0/0 (this DOES NOT equal 1)). Take, for instance, the function f(x)=(x2-1)/(x-1). If you were to plug in x=1 into this equation, you would receive 0/0 out of the function. This is an indeterminate form, which is not good and not solvable. However, unlike the asymptotic discontinuities we discussed before, this general limit does exist. If you were to evaluate from the right side of x=1, you would discover:f(2)=3f(1.5)=2.5f(1.1)=2.1f(1.01)=2.01f(1.001)=2.001As you can see, the values are approaching 2, so the limit from the right side as x approaches 1 for this function is 2. From the left, you get:f(0)=1f(0.5)=1.5f(0.9)=1.9f(0.99)=1.99f(0.999)=1.999Once again, the values approach 2, so the limit from the left as x approaches 1 is 2. Both the right and left limits equal each other, so the general limit exists, and can be expressed as "the general limit of f(x) as x approaches 1 is 2". As you can see, the funciton values need not necessarily exist for the limit at that value to exist, especially with hole discontinuities.Hopefully, through exploring different types of the more interesting types of limits, you have gained a better understanding of what a limit is and how to arrive at one. If you still require more help, message me on here.
