uses of mathematical limit in daily life
214191
You run a bank and a competing bank has a branch across the street.\n\nYou compound your interest annually. So you use the formula: A = P * (1+i)^n.\n\nThe bank across the street says, "We'll compound your interest every month. Their formulate is: A = P * (1+i/12)^(n*12), which gives the customer a little better deal.\n\nOkay, this means war. You start advertising weekly compound interest, or: A = P * (1+i/52)^(n*52), which is a slightly even better deal.\n\nThe other bank compounds daily.\n\nSo you decide to take it as far as you can go. You'll compound continuously. You're formula is:\n\nA = P * (1+i/x)^(n*x) as x approaches infinity. \n\nThe bank across the street can't beat that. Oh, there's no infinity button on your calculator, so how do you calculate savings deposits?\n\nBy running this formula through limit theory, you use the fact that (1+1/x)^x as x approaches infinity is e, and you get the following formula:\n\nA = P*e^(i*n) for continuous compounding.\n\nI don't know of any bank that calculates interest continuously, but there are at least two natural phenomenons that change at a continuous rate.\n\nThe first is population growth, such as the number of humans on the plant, or the number of bacteria in a jar.\n\nThe other is radioactive decay, which is often described as "half-life."\n\nBoth of these natural behaviors are defined by the continuous growth formula, and it cannot be derived without limit theory.\n\nBy the away, we pretty much define calculus using limit theory, but one could argue that calculus isn't part of daily life.
112000
well, you just multiply top and bottom by x, like how you simply fractions.  (clearly x isn't 0 so this is legal)\n\n= lim (x->1) x(1-1/x)/(x(x-1))\n= lim (x->1) (x-1)/(x(x-1))\n= lim (x->1) 1/x \n= 1
472119
The first five are simple\nP(5,1) + P(5,2) + P(5,3) + P(5,4) + P(5,5) \n5 + 20 + 60 + 120 + 120 = 325\n\nSix and seven are a little more complicated\n6!/2! + 7!/2!2!\n360 + 1260 = 1620\n\nEight is special because you limit the maximum.\n\nList of bad values\n9x,xxx,xxx\n7x,xxx,xxx\n69,xxx,xxx\n67,xxx,xxx\n66,xxx,xxx\n65,9xx,xxx\n65,7xx,xxx\n65,6xx,xxx\n\n8!/3!2! - (2 * 7!/3!2!) - (3 * 6!/3!) - (3 * 5!/3!)\n3360 - 840 - 360 - 60 = 2100\n\nNow add the results.\n325 + 1620 + 2100 = 4045
444076
My husband and I just used geometry the other day to estimate how much tile to buy for our 2 bathrooms.  Our bathrooms have a lot of irregular spaces, so we had to measure the entire perimeter of each bathroom.  We then split the bathrooms into different geometric shapes to find the area.  We had to work our formulas for several squares, rectangles, and triangles.   Then we added them all together to come up with the square footage.  After that, we had to estimate how many 12 inch by 12 inch tiles we needed.  It was pretty tricky, but my husband is a math whiz, so it's easy for him.  He's an engineer, go figure...
546493
lim ((arctan(x))-(pi/2))*(x) = (lim(arctan(x)-lim(pi/2))*(x)\nx->+infinity                            is this step ok?\n\nanyway: looks like it's 0*x, so 0
383727
Rule of thumb for limits:  first, try substituting the value x approaches into the function, and you'll either end up with:\n(1) some value\n(2) some value divided by 0, or\n(3) 0/0\n(4) some value divided by infinity\n(5) infinity divided by some value\n(6) infinity/infinity\n\n\nIf (1) is true, then the answer will be just that value.\nIf (2) is true, the limit does not exist.\nIf (3) is true, the limit may exist and you'll have to algebraically determine what the limit is.\nIf (4) is true, the value will be zero.\nIf (5) is true, the value will be infinity (or "does not exist" may be valid too)\nIf (6) is true, the limit may exist.\n\nCases #3 and #6 involve using L'Hospital's Rule, where you take the derivative of the numerator and denominator and calculate the new limit.\n  Let's try these tricks on each question.\n1.  Lim (x --> 1, x^1/(1-x)) \n\nIn this case, substituting 1 into the function yields 1/(1-1) = 1/0, so the limit doesn't exist.\n\n2.  Lim (t ---> 0, e^(qt - pt)/t)\n\nSubstitute 0, and you get e^(0-0)/0, or 1/0, so the limit doesn't exist.\n\n3.  Lim (t ---> pi, sin(t)/(t^2 - pi^2))\n\nSubstitute pi to get sin(pi)/(pi^2 - pi^2), and we get 0/0, so we have to proceed.\n\nUse L'Hospital's rule (it should be in your notes somewhere), where you take the derivative of the numerator and denominator of the fraction to get a new limit.  So the new limit becomes:\n\nLim (t --> pi, cos(t)/(2t)) and at this point we substitute pi, to get\ncos(pi) / (2*pi) = -1/2*pi, which is our answer.\n\n4.  Lim (t --> infinity, ln(ln(x))/ln(x))\nThis is an infinity/infinity case, so we use L'Hospital's Rule.\n\nLim (t --> infinity, (1/ln(x) * 1/x) / (1/x) ) )\n\nThat meshes into\n\nLim (t --> infinity, 1/ln(x))\n\nWhich becomes a 1/infinity case, so the answer is 0.
323459
The world around us  is in constant change and motion. Grass grows, a tennis ball flies through the air, water flows down a river, the moon appears to move across the sky. One of the most important fields of study within mathematics is CALCULUS, the study of change and motion. Calculus, perhaps more than any other field within mathematics, is a mixture of pure and applied mathematics.\n\nThe scientific field that makes the greatest use of calculus is physics. Physicists observe the motion and change of objects and create models to describe the patterns in those changes. We might want to know, for example, how fast a ball would be traveling after 10 seconds if we dropped it off a very high cliff. Calculus enables us to determine that, at any instant, the speed of a falling object is 32 times the number of seconds it has been falling. In this case, at 10 seconds the call would be travelling at a rate of about 320 feet (98 meters) per second.
26748
do you mean things as far as max and mins, asymptotes and things like that?\n\nif you are a little more specific i can help you better, or e-mail me, it would be a little easier  matttlocke@yahoo.com
43655
There are many practical applications for imaginary numbers. \n\nFirst, nothing in mathematics really EXISTS. Mathematics is just a way of creating a set of rules, then seeing what can be proven from those rules. Applied mathematics is a procedure where a subset of the material from pure mathematics is used to model something in which we are interested, which usually is something in the real world. \n\nIf the rules for manipulating things for imaginary numbers are useful, then that is a good thing. However, they are useful, because they let one solve a lot of problems easier than if we had to make more cumbersome manipulations without them. \n\nFor example, in any problem involving waves and frequencies, they are very useful, because of Euler's formula:\n\ne^(ix)=cos(x)+i sin(x)\n\nThis lets one manipulate trigonometric quantities easily in a compact form. \n\nAll of electrical engineering makes extensive use of this therefore, especially when power is involved, because AC is so prevalent. \n\nSolving many equations are far easier when imaginary numbers are used, even if the initial problem is all real, and so is the final answer. \n\nIntegrals that are used in all application areas are sometimes far more easily solved using complex integration. \n\nAll of quantum mechanics is deepy connected with imaginary numbers. The Schrodinger equation contains imaginary numbers. The answers are complex functions. Their modulus squared produces the real probability functions we use. \n\nImaginary numbers are used throughout physics. \n\n \nTo paraphrase a famous saying, the quickest way to real results is through the complex plane. \n\n(the real quote by Jacques Hadamard is more accurately translated as "The shortest path between two truths in the real domain passes through the complex domain.")\n\nThe more important question underlying this, is, why is mathematics so unreasonably effective at modelling things we are interested in? (see references).
449460
Numbers never end because for any one we care to name, we can add something infinitely large or small to it to produce still another number which is larger than the first. \n\nSome mathematicians may dispute your assertion that we don't need that many numbers, because what might not be practical today can turn out to be years or centuries down the road.  For example, the development of the concept of infinity ultimately led to the development of the calculus, a powerful tool in just about every advanced and worthwhile endeavor undertaken by man.
537607
Use L'Hospital's rule twice and get e^x/2 which has a limit of infinity.
616354
Math is used all the time in the engineering sciences.  Many physical phenomena, including fluid flow, heat transport, and diffusion can be described by appropriate partial differential equations.  In order to solve these equations and make predictions, you need to be good at calculus.\n\nIf you limit yourself to addition, subtraction, multiplication, and division, you would be stuck with linear models for everything.  This means that any more complicated relationship between two variables could not be modeled continuously, and you would never be able to extrapolate with any confidence.  Thus development of new technology would be strictly trial and error (and you wouldn't even have a good trial and error system without statistics).\n\nHang in there!  Get through that math.  You don't have to like it, but you will inevitably appreciate the developments that math has enabled.
303543
Only numeraries use them. They don't have to buy them. And they don't wear them outside of their homes.
70545
You prove that for any tiny little e>0 you pick, there exists a little d>0 such that \n\nif abs(1/(x^2)-1/x^2))<e, then abs(x-x)<d,\n\nand since x-x=0 (this is a trivial limit unless you've messed up the parentheses in the problem), just let d=e, or e/2, or any value between e and 0.
210639
Zeno ignored the fact that the infinitely many smaller steps take infinitely less amounts of time to do.\n\nAs the earlier answerer pointed out, sum the power series and you get a finite value for the time taken...\n\nLike a lot of these logical tricks, there's something being forgotten or ignored to make it look impossible.
165215
Is this (x + 3)/[x*(x - 1)^2] ? In that case, the limit is as you stated, positive infinity. \nA limit is never undefined; it either exists, or it does not exist. In the special case that it does not exist and it increases without bound or decreases without bound from all approaches, we say the limit is positive or negative infinity respectively.\nAs always, when a limit diverges, look at the behavior of the expression in an arbitrarily small region around the limit point (in this case, x=1). Since the denominator is a square multiplied by x, it is never negative in a sufficiently small neighborhood of 1 (specifically, any neighborhood contained in the interval (0,infinity) ). Similarly, the numerator is never negative in a sufficiently small neighborhood of 1, so the behavior of the whole expression is to diverge to positive infinity, no matter how it is approached.
361031
Oh Dear! lots of dodgy maths out there!\nWelcome to Mr Cantor's infinity paradise hotel!\nWe got infinite rooms, but they're all full just now.\nDon't worry!.. we'll squeeze you in!..I'll just get every guest to move one room along\nNow you can get in room1\nHey there's an infinite stretch limo arrived with an infinite number of guests..no probs just get all our guests to move from room n to 2n!\nYes infinity is an uncountable number, but you can still do mathematical ops with it\nHope that helps, you can work out the rest foor yourselves. PS always agree with your wife- she's right even when she's wrong-now that's a true paradox