Analysis and Calculus

I need help proving that LHS=RHS in the following: a) b) I don't believe that either is difficult to prove, but the problem is that neither first nor second year engineering maths taught me enough to be able to do this. I'm sure there are identities I'm not aware of... I'd prefer to be pointed to the right place where I can learn enough to do this myself, but then again, given the nature of the problem, even someone showing me exactly how these proofs are done would be beneficial enough. Thanks in advance! (I need to have this sorted out before Feb 26)

The problem reads: Use seperation of variables to solve the initial value problem dy/dx=x-4+xy-4y; y(0)=4 and also stuck with \int_a^b x^2 lnx\,dx any sugestions?

The formula for the derivative is lim (f(x+h)-f(x))/h h->0 But is there a similar formula for finding indefinite integrals? Help!

Hey guys, I could really use some hints on how to solve the integral [math] \int \frac{x}{1+\sqrt{x}} dx [/math] I tried some substitutions, and doing some manipulations on the expression, with no solution. Any help would be much appreciated. Regards, Kerbox

Hi everyone, I understand (or should I say "know") the theoretical proof of L'Hopital's rule, but the flipping of equations is not really satisfying my curiosity... my question is that is there any way to picture L'Hopital's rule? by picturing I mean is that we could picture the derivative of a function as h approaching 0 as (x, x-h) gets smaller and smaller, then is there similar or totally different way to picture this rule, or maybe any calculus or even any higher math problem that is only based on equations...? i hope you understood the point of questions, if not please ask me thx!

I know that the intregation of [math]\frac{sinx}{cos^2x}[/math] is [math]secx[/math]. But I'm not sure how to get to the answer. I started off by using the trigonometric identity: [math]cos^2x + sin^2x = 1[/math]. Therefore, [math]\frac{sinx}{1-sin^2x}[/math]. Now what?

I started to solve this equation but it seems I'm doing something wrong. Here s the equation: cos^3 x-3cos^2 x+ cos x = 2cos(x/2 + pi/4)sin(3x/2 - pi/4) I got the first solution X1= (2n+1)pi/2 The second solution according to the book: X2=2pi*n

hi every body how can i derivative (n) times this function e^(1/x)???? thanks alot 4 all

Ok Guys, you have to admit, these forums are pretty quiet for some reason. Im going to post a problem for someone to figure, ill start off relatively easy: [math](\sum_{n=0}^{m} 10^n)^2[/math] Gives what general Form? Its ok if you can spot the pattern, but try to prove it as well.

Is it possible to integrate sqrt(sin x) My teacher told, its not? Why? If it is inegrable, how? Thanks!

What is the best strategy to take towards a Geometry-Related Proof?

why is the spherical volume element r^2 sin phi dr d phi d theta ? and not r^2 dr dphi d theta ? it doesn' make sense to me as r theta is the arc length in a circle and so r^2 theta x phi should give the area element for a sphere, and then why not just allow for an infinitesimal amount of depth with dr and then declare that the volume element? also why is the angle phi drawn off the z axis and not the x axis like theta is?

Well, I'm supposed to compute the drag coefficient of a sphere in a hypersonic newtonian flow. In a newtonian flow the pressure coefficient is given by: [math]C_p = sin(\alpha)[/math], with alpha the angle of attack. The pressure coefficient on the lee side is 0. Now. My problem is that I have to compute the total drag coefficient, integrating a surface integral over half a sphere. The final drag coefficient is supposed to be 1, but I just can't get it right , and my calculus book is a good 1000km away... Could someone help me out? Thanx a lot!

I have to take the FE in April and haven't had a math class since 2001, so can someone please jog my memory on this one: How fast is the distance of an airplane from a fort increasing 1 minute after passing directly over the forst at a height of 10,000 feet when it is flying horizontally at the rate of 200ft/sec? I used the right triangle with side a = 10,000 ft and side b = 12,000 ft (from 60 sec * 200 ft/sec). C is the distance of the plane from the fort. c = sqrt(a^2 * b^2). I solved for dc/db, is this correct? I ended up with: dc/db = b ---------------- . sqrt(a^2 + b^2) If I plug and chug from here, I don't …

I need a tiny bit favour from you guys. Given that [math]f(x)=\frac{x-1}{(x+2)^{50}}[/math]. The solution is [math]f'(x)=\frac{52 - 49x}{(x+2)^{-51}}[/math]. Am I correct? Because the teacher had this solution: [math]f'(x)=\frac{52-49x}{(x+2)^{51}}[/math]. Who is right?

Is there a certain strategy or way to solve these because they take a really long time. Im sure this stratgey would also work for inverse matricies.

hello everyone! I am having really a hard time "understanding" what do we mean when we say 'integrate a function'.. I know it's a backward derivative, anti derivative, but I don't understand "how" it is.. for example, i know and I "understand" that derivate of a function is the rate at which that function changes, and it's calculated by taking a limit of zero to a specific point...but integration is really burning my neurons... also, do u know any good website which shows analytical approach to solve for definite and indefinite integrals.?? or if possible, could someone explain?

Ok, obviously, sine is a function. But what I really want to know is what is going on under the hood of sine. What equations and algorithms make up sine? I have searched the web, but I am not sure what to search for and haven't come up with anything useful. I have grepped math.h, but to no avail. Any help is much appreciated.

How do you solve a 4 variable system with 4 other systems involved? What is the best apporach in solving it. -Thanks for the Help

Find the general sollution to [math](x+y)\frac{dy}{dx}=x^2 + xy +1[/math] using the substitution of [math]y=v-x[/math] Using that [math]\frac{dy}{dx}=\frac{dv}{dx}-1[/math] I plugged that in to get:[math]v(\frac{dv}{dx}-1)=x^2 + x(v-x)+1[/math]. Which rearanges to [math]\frac{dv}{dx}-\frac{1}{v}=x+1[/math]. But from that point I don't know where I'm going. Could anyone give me a nudge in the right direction?

OK, I have a stupid question, but if one had the equation: [math]\delta (g^{ij}(t+\delta t))/\delta (g^{ij}(t))[/math] wouldn't that be equivalent to [math]\partial_{t} g^{ij}(t)[/math] and thus definitionally [math] -R^{ij} [/math] via the definition of the Ricci flow?

So I thought I had a good grasp on rotating functions and evaluating volumes, but apparently not. I'm having trouble picturing the cross sectional area of a 2-d graph. I get that when you have a volume (3-d) of say, a sphere, the cross sectional area is simply a circle, or when you have a cube, the cross sectional area is simply a square. But the 2-d graphs confuse me. Like the bottom two graphs on this page: http://www.pinkmonkey.com/studyguides/subjects/calc/chap8/c0808301.asp Could anyone help me picture why the one graph has a cross sectional area of a circle and why the other has a cross sectional area of an equilateral triangle, thanks...

I'm confused about something we learned in Calc today and thought someone could explain it a little. We're doing arc lengths and now the surface area of a solid formed by revolving a curve. Given any function [math]f(x)[/math] revolved about the x axis, We treated the surface area as a lot of circumferences stacked next to each other, with the radius equal to y. My teacher showed us the formula to be [math]\int_a^b f(x)2\pi\,ds\[/math] I understand the concept of ds I think, but I don't understand is why you have to use ds and can't use [math]\int_a^b f(x)2\pi\,dx\[/math]. I pictured this problem as finding the circumference then multiplying it by thickness dx to…

Hi, I need help with this question At a publicity event, Ayida, a stuntperson, will jump out of a helicopter with a jetpack on her back. The jetpack allows her to achieve a net upward acceleration of 4.4m/s^2 for a single interval of maximun lenght 10s. Ayida wants to time the use of the jetpack so that she lands with a zero velocity. a) If the helicpter is 100m hight, when should Ayida turn on her jetpack? When will she land? b) If the helicopter is 200m hight, when should Ayadia turn on her jetpack? when will she land? c) What is the maximum height from wich Ayida can jump to land with zero velocity? I don't know where to start can someone explain this proble…

So I got this HW assignment and i was wondering if anyone could confirm my anwser. Here's the question: The population, in thousands, of Mathville is modeled by the equation P(t) = 20(4t+3)/(2t+5), where t is the time in years since 2005. The question is...what is the population growth rate in 2006. So then I took the formula and found the first derivative, which i found to be 280/(2t+5)^2, and then set the first derivative to equal 0 so i could solve for t. In the end I got 0 = 280. Now i know that doesnt seem right. Can anyone help me? PS- on the following question i concluded that the population will never reach 50000 because there is a horizontal asymptote at y=4…