Analysis and Calculus

in proving the cancellation law in inequalities in real Nos we have the following proof: Let : ~(a<b) Let : a+c<b+c Since ~(a<b) and using the law of trichotomy we have : a=b or b<a for a=b => a+c=b+c.....................................................................(1) for b<a => b+c<a+c......................................................................(2) and substituting (1) into (2) we have : a+c<a+c ,contradiction. Hence ~(a+c<b+c) Thus by contrapositive we have: a+c<b+c => a<b is that proof correct??

Something that should be punched into college computing systems although out the nation:<br><br> If m is a counting number, of the set 1,2,3etc and m=n-1 And we assume that (-1) (-1) always equals = -1 (and is not equal to 1) Then (m-n)(m-n) shall always equal the negative opposite of a prime or relitively prime number! A prime number being one that is only divisible by itself and the number one! A relative prime being the number that can only be expressed as the product of two primes and no more. Examples: (1-2)(1-2)=1-2-2-4=-7 (prime) (2-3)(2-3)=4-6-6-9=-13 (prime) (3-4)(3-4)=9-12-12-16=-31 (prime) (4-5)(4-5)=16-…

One can derive the formula for the area enclosed by a circle using the elementary method with integration. I thought about applying the same idea to spheres, except this time I assumed the final formulae to be true, and then try to get the differentials separated to see how it works out conceptually. Now that I've gotten the differentials, I'm wondering if there's any intuitive visualization behind these identities. First, surface area. Now, it doesn't make much sense for the radius to be multiplied by its change length. One could instead consider [math]C=2\pi r[/math] in regards to the great circle of the sphere. Where [math]\mbox{C}_{\mbox{p}}[/math] de…

I cannot find any way possible to prove any of these two concepts to exist in our three dimensional world. So, therefore I would like someone to prove that either one or both of these concepts actually exist in our three dimensional world. My only way that I can prove the concept of infinity would be a transition between dimensions. For instance, if you have a 2D square, and cut all of it into 1D lines, which is not physically possible, only theoretically, you would obtain infinite 1D lines, as they have no width to remove from the 2D square.

Maybe should have gone in biology... @#$%! I posted this on another forum, but I'm hoping to get better responses here. I got my understanding of the ACE model from Wikipedia, so it might be over simplistic or just wrong. https://en.wikipedia.org/wiki/Twin_study#Methods my understanding of the ACE model: Pasted from the other forum website for convenience. I wrote it. Dizygotes (fraternal twins) and monozygotes (identical twins) are used to calculate the relative contributions of "additive genetics" and "common environment". Here's how. The equation assumes that all twins share 100% common environment ( C), but dizygotes only share ~50% of the…

Hey people, we are new to this forum! We are two students from environmental sciences and we created a graph that we can't interpretate. We put this in "analysis" because we think that is a very complicated graph from a strange equation, so, we think this is the better place. If we are not right, please tell us! Well the fact is that we were using "R" to study ecology population of some fish specie. We created a vector to study the population increase in a empty river starting from 100 individuals. Then we used the eigen analysis (eigen matrix) to know the transition matrix of that population in 50 years. Then, we plotted the eigen analysis, and we came out with our unk…

What would be the thickness of the coin (disk or cylindrical) with 1 unit diameter that would make the tail /head/body(side) outcome be a fair 1/3 probability?

Hi. In the formula E = V B L for the "Conclusions" paragraph at near bottom of page ----> http://cfpub.epa.gov/ncer_abstracts/index.cfm/fuseaction/display.abstractDetail/abstract/8630/report/F B being 0.00004 Tesla, V being 2 metres/second, L being 300 metres; Should the V,L units be in centimetres or metres for E to be Volts ? [ Did not copy and paste the pertinent portion here because figure 4 shows 'Copyright' ]

In revolution of solids: What variable you integrate with respect to, i.e. the independent variable, matters. But in revolution of surfaces, the variable you integrate with respect to doesn't matter. Why is that? E.g., you have a segment of a graph bounded by [latex] y=x^2 [/latex] and [latex] y=1[/latex]. You rotate this about the y axis. To find the area of the solid, you integrate: [latex] \int_0^{1} \pi y\,dy[/latex] Where you have to use the variable y because the radius is in terms of x, and at different values of y, the value of x stays near different values longer because the graph is curved. i.e., the values of x, the radius, would be different from …

When we think of a tangent line of a point on a curve as only touching that curve at one point, while still having a fixed slope, we have already shed light on the nature of lines and the Euclidean grid: if you were to begin rotating the tangent line, at what point would it cease to be a tangent line and become a secant line? It would become a secant line the instant it began rotating, as lines are infinitely thin. This notion of infinitely thin lines, and infinitely small increments of time, is at the heart of calculus. Why is this ever counter-intuitive to us? It has been argued that, hundreds of years ago, "math-denial" was a means for rejecting the idea of change …

Hi, Hello, I just had a small question about assumptions in mathematical word problems. Suppose you are given a calculus problem (related-rates), "A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?"(Larson Calculus P 153) This is a quoted problem from Larson's Calculus 10th Edition. My question is here: Why do you assume for example that there is no hole from, which air LEAVES? Basically, in general, why do you make unstated assumptions for example, there is no air leaving, or the balloon doesnt explode…

Hi everyone. I am Ricardy Ricot. I created an android app that randomly changes it's background image to an image of calculus formulas/equation taken from calculus 1 every time you click/tap on the screen. It chooses randomly between 104 formulas. It acts like flashcards in a sense. However, the idea was not to memorize those formulas, but to have them at your fingertips wherever you may be so you can think about them and see the ramifications that they imply. And I think that the fact that it is random spices things up. You can never be sure which formula you will see next. This app can be downloaded from this github link (free of charge): url deleted You w…

Today I want to share what Is BODMAS Rule & How to use it? BODMAS rule decides the order of operations for add, subtract, multiply, divide, etc as below shown B-Brackets (do all operations contained in the brackets first) O-Orders (powers and square roots etc) D-Division M-Multiplication A-Addition S- Subtraction Lets see an example and check how BODMASS Rule works 30-(2*6+15/3) +8*3/6 Step1: Brackets 2*6+15/3 = 12+5 = 17 Step2: Division 30-17+8*1/2 Step3: Multiplication 30-17+4 Step 4: Addition and Subtraction 30-17+4=17 20+30-5/4*2+ (1+6) (5-6/4)+9*7 1-6*(2+9)/8 BODMAS Rule is very helpful in solving various algebr…

When we discuss angles in mathematics we consider anticlockwise angles as the positive direction of rotation. In particular this is carried through to phasor theory in electrical engineering and many other fields. But when mathematicians and physicists discuss rotational symmetry the clockwise rotational direction is chosen as positive. eg http://www.mathsisfun.com/geometry/symmetry-rotational.html Is this anomaly not potentially confusing for young minds?

Hi folks. I recently had a long trip, driving and counting the remaining miles and thought up a funny riddle: suppose you drive and reach a sign that says your destination point is 142 kilometers away. You then proceed forward at a speed of 142 kilometers per hour. Next sign comes up and says the destination point is now 141 kilometers away. You immediately drop the speed to 141 kilometers per hour and drive on. You keep going like that and eventually reach a point that says "1 kilometer" and you walk towards the destination at 1 kilometer per hour, and naturally the last 1 km takes 60 minutes. So I wondered if there was a way to put it into a formula or maybe a way to ca…

Hi, Im a 31 year old computer programmer that want to revive some the calculus i learned at school, and learn new things as I go on. I seem to grasp things very fast as I remember while reading the tutorial here on the forum, but I need some help to check wether i have done those calculations right. I've read to lesson 6 for now and will continue if i get some answers of my questions here. Great tutorials by the way! I wonder what the final answers in those examples are. example lesson 5 (quotient rule): : 6 / (x2 + 16) example lesson 6 (chain rule): : 48x^8-33614 for number one exercise (in lesson 6) i get: = 6x2+23 for number two exercise i get: = …

How would I find the area shaded in blue below? (please forgive how big the image is) I'm assuming you'd have to use calculus as there is no way to simply subtract the area of the circle from the area of a larger rectangle without ending up looking for a limit. I guess I don't know how I'd go about finding the anti-derivative of a circle.

is it infinity or 1 or 0 or N.D???? Bro plzzz help meeeeeeeeeeeeeeeeeee

I need the real meaning of maths 'lets see which one is the best answer'

From the usual epsilon, delta definition of continuity, two significant theorems follow : (i) a function continuous on a closed interval attains in supremum and infimum on that interval ; and (ii) for any two values in the range of the function, any intermediate value also belongs to the range. From these theorems, one can deduce that the image of any sub-interval of the domain is a sub-interval of the range. And it turns out that this is a necessary and sufficient condition for continuity. So we can use this last as the very definition of continuity for a function on a closed interval. Some students, who find the conventional definition of 'continuity at a po…

Full disclosure: I am no mathematician. The furthest I got in high school was Algebra 2. One of my favorite movies is The Manhattan Project. I want to build a prop replica of the device is the movie. I even plan to build the circuitry with discrete logic instead of a microcontroller. In the film, the device malfunctions due to radiation and its timer circuit begins to count down from 999h:99m:99s. The countdown increases exponentially. I would like to know the time to zero starting from 999:99:99 and possibly graph the decay rate over time. In the film, the formula "As y approaches infinity t = (1 + (1 over / n ))to the nth." Some google-fu leads me to i…

Hi I am not very advanced in calculas. I need to solve for X(t)/Y(t) when t -> infinity. X'(t)+aX(t)+cX(t)-bY(t)=0 ....1 X(0)=0 Y'(t)+bY(t)+cX(t)=0 .....2 Y(0)=0 So I thought of deriving both equations to get: X''(t)+aX'(t)+cX'(t)-bY'(t)=0 ...3 Y''(t)+bY'(t)+cX'(t)=0 ...4 Then substituting 2 into 3 & substituting 1 into 4 X''(t)+aX'(t)+cX'(t)-b*[bY(t)]-bcX(t)=0 ....5 Y''(t)+bY'(t)+cX(t)[a+c]+bY(t)=0 .....6 Then substituting 1 into 5 Then substituting 2 into 6 X''(t)+aX…

Hello. I'm studying for my analysis final and I have no idea how to do this problem. It says the following: Suppose f(x)=x^3+3x^2-2x-1 is continuous everywhere on R. Use the intermediate value theorem to show that f(x) has three distinct real roots. Hint: Evaluate f(x) at x=-1,0, an 1 and make use of the limit behavior of f(x) as x approaches plus or minus infinity. I calculated the values and got that f(-1)=3, f(0)=-1, and f(1)=1. Also, as x approaches negative infinity, f(x) approaches negative infinity and as x approaches positive infinity, f(x) approaches positive infinity. When I graph it, I can see that there are three real roots but I just don't know how t…

Could I sum a series of points to sum a series of lines to make a plane, then sum a series of planes to make a solid object, then sum solid objects over different 4-D intervals to create a 4-D object? Or in other words, is there a direct way to sum a bunch of 1 dimensional points into a 3-D or 4-D object?

Lately I've been arguing with one of William Lane Craig's drone lackeys on his Facebook page. On the one hand this person is reciting the common mantra that 'infinities cannot exist in reality', and on the other hand he is claiming to hold to a classical view of space-time. When I pointed out to him that these two views are incompatible since if space truly is classical in nature then there would be an actual infinity quantity of spatial locations within space-time, he retorted that that is 'just a potential infinity, not an actual one!' Now, I think I know enough about calculus to be pretty sure that he is simply misusing terms here, but on the off chance that I am t…