Analysis and Calculus

Hi there, I wanted to learn some calculus for statistics but it seems like pre-calculus will take many months. If you look at this page from Khan Academy, it does not look like it will be something I can understand for a long time: Precalculus | Math | Khan Academy I was wondering if the path to calculus would be shorter if there is something very specific I want to achieve. What I would like to do is learn one aspect of statistics through calculus - would anyone be able to offer me a roadmap for that? You can choose the part of statistics that the roadmap applies to. My overall goal is to have a very strong understanding of statistics and eventua…

Introducing The Most Fastest Way to Find Perfect Square Roots. Creating Successive Series Beforehand. 0 -- 1 has zero difference. 1 --- 3 has only as difference of one. 3 ---- 6 has a difference of two. 6 ---- 10 has a difference of three. 10 ---- 15 has a difference of four. . . . This series is a form of infinite successive series where integers at the right hand side of the below series, that is 1, 3, 6, 10 15…. (highlighted below in yellow color) is the result of addition of positive integers in following sequence such as 2, 3, 4, 5, 6, 7, 8….(highlighted below in green color) 0 -- 1 + 2 1 --- 3 …

There are many units to calculate distance, I am working in construction industry, so calculating distance is very frequent. I still usually spend a lot of my time calculating and converting distance units. I am looking for a way to save time converting distance units. Is there a software on the phone or a website that can do that? I often have to convert from centimeters to inches , cm to feet, centimeters to inches,..vv Can someone recommend me a solution to this problem?Thanks everyone

My son’s 3rd grade math is always asking him questions about measurements and equivalents. He always comes and asks me for help when there are questions like: How many quarts in a gallon? (A gallon is equal to 4 quarts) How many cups are in a gallon? (There are 16 cups in a gallon) How many cups in a pint? (There are 2 cups in a pint) How many cups are in a quart? (4) When I taught foods classes at a high school, these measurements always seem to be a challenge, too! Someone have a fun and easy way to help teach these measurements?

I'm working on weight. I often have to convert ounces to grams or grams to pounds. Here's how I usually do it: write the numbers down on paper, find the formula, and then enter the numbers into the calculator. Everything seems complicated and takes my time, it makes my work slow and inefficient. I am looking for a software or a website that allows me to convert easily and quickly. Can anyone recommend it to me. Any suggestions are always helpful. Thanks everyone

Differentiate: \[ f\left(x\right)=\log_{x}\left(\sin x\right) \] Solution: Spoiler \[ y=\log_{x}\left(\sin x\right) \] \[ x^{y}=\sin x \] \[ e^{y\ln x}=\sin x \] \[ e^{y\ln x}\left(y'\ln x+\frac{y}{x}\right)=\cos x \] \[ y'\ln x+\frac{y}{x}=e^{-y\ln x}\cos x \] \[ y'\ln x=e^{-y\ln x}\cos x-\frac{y}{x} \] \[ y'=\frac{1}{\ln x}\left(e^{-y\ln x}\cos x-\frac{y}{x}\right) \] \[ y'=\frac{1}{\ln x}\left(e^{-\ln x\log_{x}\left(\sin x\right)}\cos x-\frac{\log_{x}\left(\sin x\right)}{x}\right) \] Simplifications: \[ e^{-\ln x\log_{x}\left(\sin x\right)}=\l…

If you look at the graph of sin (x) you see that all the zeroes are located at multiples of pi. So if you were to factor sin (x) as if it were a polynomial you would get m * x * (x-pi) * (x + pi) * ( x-2pi) * (x + 2pi) * ( x - 3pi ) * (x + 3pi) ..... (x - n pi) * ( x + n pi) as n approaches infinity. Question: what is m? I figured this much from computer experiments, m is not a constant, it is a function of x and n. m is less than 0 if n is odd, m is greater than 0 if n is even. If you graph abs (x) and scaled it by the appropriate very large factor you'd see that m (x) looks like a bump centered at x =0 which morphs as n increases, it retains the bump fi…

Infinity plus Anything, call it Infinity + 1 = Infinity but Infinity - 1 = less than Infinity. Is that possible ?

hi,I need the answers of quuestions given below (one of my colleague asks, I could not find at its first look line) 1) limx→∞(2−x+1)x 2) the graph for 2xx2+1 sorry I could not set the formula in the new version of this website. 1) lim x to infinity (2^-x+1)^x 2) the graph for 2x / (x^2+1)

Find the volume V inside both the sphere x2 + y2 + z2 = 1 and the cone z = [math]\sqrt{x^2+ y^2}[/math] How to use change of variables technique in this problem?

My scribblings came up with the following interesting function f(x1,x2,... xn) = -ln(x1^x1*x2^x2*,... xn^xn) Where: x1+x2+... xn = 1 0<xi<1 I suspect that this function ranges 0 to ln(n) but a proof is beyond me. Assistance would be most appreciated.

Hi,

Sufficient conditions for a critical point at (a, b, c) to be a local maximum or local minimum of a smooth function f(x, y, z).i-e [math]\nabla {f} (x,y,z)=0[/math]. How to define D in case of three variables namely x,y, z.

If one were to turn up the volume of music and then turn it down again very quickly (say with infinite speed), will the part where he turns it up even exist? Would the change in volume even exist? So does 2*infinity = 0? I initially posted this on 4chan's science board but never got any good answers or ideas how to solve this problem. https://boards.4channel.org/sci/thread/14349334#p14349347

I know the answer to question 8. But how to answer question 9.

While playing in my mind with a question from another thread, the one about n choose k calculation, it occurred to me that it could be solved via a following recursive equation (regardless of the standard derivation of the well known formula for n choose k). If we select any one element out of n, all groups of k are of two types: the ones that include the selected element and the ones that don't. There are C(n-1,k-1) choices for the former and C(n-1,k) for the latter. Thus, we get this recursive equation: C(n,k)=C(n-1,k-1)+C(n-1,k). There are two variables there, so perhaps we need two boundary conditions. These could be, e.g., C(n,1)=n and C(k,k)=1. It is …

I am working on a TI Inspire video game, in which the player is in a dark room holding a flashlight. The flashlight is located at the player's eye and is pointed in the look direction. I render the light by coloring in the conic sections formed by the intersection of each wall, floor, or ceiling and concentric cones of light starting from the innermost cone working outward. As it turns out whenever the conic section formed is an ellipse, it appears to transform into a perfect circle located at the dead center of the viewport after performing the perspective rotations and z divide. This appears to always be the case regardless of the relative position and orientation of …

A cool little example of common confusion with partial derivatives, from Penrose's "The Road to Reality" (he attributes the words in the title to Nick Woodhouse.) Let's consider a function of two coordinates, f(x,y), and a coordinate change X = x, Y = y + x Because the X coordinate didn't change and is the same as the x coordinate, one could expect that the corresponding partial derivatives are the same, fX=fx. And, because the Y coordinate is different from the y, these partial derivatives, fY and fy, could be expected to differ. In fact, this is just opposite: fX=fx-fy fY=fy The confusion is caused by the notation: fX does not mea…

Can the thing in the title be rational?

Momentum is used to sense the amount of force applied to a moving object. With the help of Momentum, you can know the nature of the applied force on an object. Momentum is usually represented by the product of the mass and velocity of a moving object. But in this case of quantum mechanics, the equation of momentum will be different. How is this computed? How is this momentum computed in Quantum mechanics?

I already know that if I have a triangle with vertices v0, v1, v2 in property p0, p1, p2 then the property linearly interpolated at location l = a*p0 + b*p1+(1-a-b)*p2 a=(area of triangle formed by the points v1, v2 and l) / (area of the triangle formed by points v0, v1, v2) b= (area of triangle formed by the points v0, v2, and l) / (area of the triangle formed by points v0, v1, v2) My question is how do I generalize this to a higher order interpolation method? In my problem the property p = the normal vector to a surface and I have already calculated the Gaussian curvature of the surface to decide whether to subdivide the triangle into more triangles…

For simplicity, I am only using second order NURBS. I have a NURBS surface which essentially takes the form of x(u,v) and y(u,v) and z(u,v) are all quadratic functions of u and v. Would I be correct to say that there exists a quadric of the form 0=ax2 + by2 + cz2 + dxy + eyz + fzx + gx + hy + iz + j which is equivalent to the parametric representation? I tried applying Kramer's rule to interpolate the test points along the parametric representation but the determinant of the 9x9 matrix = 0 and I get a divide by 0 error.

My son asks How do I enforce continuity in a grid of Bezier surfaces? I know that the two adjacent control points at the border of a Bezier curve have to be co-linear in the one-dimensional case. But how do I extend this to surfaces in three dimensional space? Which points would have to be co-planar?