 # Get college calculus homework help

Recent questions in Calculus and Analysis Quintacj 2022-05-24 Answered

### How to solve this differential equation:$x\frac{dy}{dx}=y+x\frac{{e}^{x}}{{e}^{y}}?$I tried to rearrange the equation to the form $f\left(\frac{y}{x}\right)$ but I couldn't thus I couldn't use $v=\frac{y}{x}$ to solve it. Nerya Fozailov 2022-05-23

###  Timiavawsw9 2022-05-23 Answered

### Find the limit of:$\underset{x\to \frac{\pi }{3}}{lim}\frac{1-2\mathrm{cos}x}{\pi -3x}$ res2bfitjq 2022-05-23 Answered

### I have a first order PDE:$x{u}_{x}+\left(x+y\right){u}_{y}=1$With the initial condition:I have calculated result in Mathematica: $u\left(x,y\right)=\frac{y}{x}$, but I am trying to solve the equation myself, but I had no luck so far. I tried with method of characteristics, but I could not get the correct results. I would appreciate any help or maybe even whole procedure. seiyakou2005n1 2022-05-23 Answered

### In my differential equations book, I have found the following:Let ${P}_{0}\left(\frac{dy}{dx}{\right)}^{n}+{P}_{1}\left(\frac{dy}{dx}{\right)}^{n-1}+{P}_{2}\left(\frac{dy}{dx}{\right)}^{n-2}+......+{P}_{n-1}\left(\frac{dy}{dx}\right)+{P}_{n}=0$ be the differential equation of first degree 1 and order n (where ${P}_{i}$ $\mathrm{\forall }$ i $\in 0,1,2,...n$ are functions of x and y).Assuming that it is solvable for p, it can be represented as:$\left[p-{f}_{1}\left(x,y\right)\right]\left[p-{f}_{2}\left(x,y\right)\right]\left[p-{f}_{3}\left(x,y\right)\right]........\left[p-{f}_{n}\left(x,y\right)\right]=0$equating each factor to Zero, we get n differential equations of first order and first degree.Let the solution to these n factors be:Where ${c}_{1},{c}_{2},{c}_{3}.....{c}_{n}$ are arbitrary constants of integration. Since all the c’s can have any one of an infinite number of values, the above solutions will remain general if we replace ${c}_{1},{c}_{2},{c}_{3}.....{c}_{n}$ by a single arbitrary constant c. Then the n solutions (4) can be re-written asThey can be combined to form the general solution as follows:Now, my question is, whether equation (1) is the most general form of solution to the differential equation.I think the following is the most general form of solution to the differential equation :If (1) is the general solution, the constant of integration can be found out by only one IVP say, $y\left(0\right)=0$. So, one IVP will give the particular solution. If (2) is the general solution, one IVP might not be able to give the particular solution to the problem. kunyatia33 2022-05-23 Answered

### Given is the sequence ${x}_{1}=0,\phantom{\rule{thickmathspace}{0ex}}{x}_{n+1}=\sqrt{2+{x}_{n}}$. Prove:$\underset{n\to \mathrm{\infty }}{lim}{2}^{n}\sqrt{2-{x}_{n}}=\pi$Hint:Use the following formulas:$\mathrm{cos}\left(\frac{x}{2}\right)=\sqrt{\frac{1+\mathrm{cos}x}{2}}$$\mathrm{sin}\left(\frac{x}{2}\right)=\sqrt{\frac{1-\mathrm{cos}x}{2}}$Any idea how to solve this problem? Angel Malone 2022-05-23 Answered

### What is the polar form of $\left(216,-6\right)$ ? res2bfitjq 2022-05-23 Answered

### For $f\left(t\right)=\left(\frac{1}{t},-\frac{1}{{t}^{2}}\right)$ what is the distance between $f\left(2\right)$ and $f\left(5\right)$? Monserrat Sawyer 2022-05-22 Answered

### Differentiate the parametric function and find dy/dx and ${d}^{2}y/d{x}^{2}$Differentiate the parametric function and find $\frac{\mathrm{d}y}{\mathrm{d}x}$ and $\frac{{\mathrm{d}}^{2}y}{\mathrm{d}{x}^{2}}$ in terms of "t" when:$x=\frac{1}{t-1}$ and $y=\frac{1}{t+1}$I have first started by finding $\frac{\mathrm{d}y}{\mathrm{d}x}$ by finding $\frac{\mathrm{d}x}{\mathrm{d}t}$ and $\frac{\mathrm{d}y}{\mathrm{d}t}$ which comes to$\frac{\mathrm{d}x}{\mathrm{d}t}=\mathrm{ln}|t-1|$and $\frac{\mathrm{d}y}{\mathrm{d}t}=\mathrm{ln}|t+1|$and used $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\mathrm{d}y/\mathrm{d}t}{\mathrm{d}x/\mathrm{d}t}$, which gives$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\mathrm{ln}|t+1|}{\mathrm{ln}|t-1|}$ now if I divide them by each other doesn't it equal to 0? What have I done wrong here? Ryker Stein 2022-05-22 Answered

### Find${\int }_{a}^{b}\frac{1}{\sqrt{\left(x-a\right)\left(b-x\right)}}dx$ Jordyn Calhoun 2022-05-22 Answered

### Limit of $\underset{x\to {\frac{5\pi }{2}}^{+}}{lim}\frac{5x-\mathrm{tan}x}{\mathrm{cos}x}$ Isaiah Owens 2022-05-22 Answered

### How do you write the cartesian equation for $x=t-2$ and $y=-\left({t}^{2}\right)+t+2?$ Angel Malone 2022-05-22 Answered

### How do you find the angle between the planes $2x+5y-z=6$ and $3x-2y+6z=10$ ? Ryker Stein 2022-05-22 Answered

### Integrate $\int \frac{1}{1+\mathrm{sin}x}\phantom{\rule{mediummathspace}{0ex}}dx$ using substitution $u=1+\mathrm{sin}x$ Monfredo0n 2022-05-22 Answered

### What is the polar form of $\left(-1,121\right)$ ? cyfwelestoi 2022-05-22 Answered

### I have to prove, without L'hopital rule, the following limit:$\underset{x\to \mathrm{\infty }}{lim}\sqrt{x}\mathrm{sin}\frac{1}{x}=0$I tried doing a variable change, setting $t=\frac{1}{x}$ and reaching the following:$\underset{t\to 0}{lim}\sqrt{\frac{1}{t}}\mathrm{sin}t$But I can't prove neither. Simone Werner 2022-05-22 Answered

### Find all functions f(x) defined on $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ which has a primitive F(x) such that$f\left(x\right)+\mathrm{cos}\left(x\right)F\left(x\right)=\frac{\mathrm{sin}\left(2x\right)}{\left(1+\mathrm{sin}\left(x\right){\right)}^{2}}.$Hence F satisfies a first order linear differential equation in F with integrating factor ${e}^{\mathrm{sin}\left(x\right)}$So i have to integrate$\frac{2{e}^{\mathrm{sin}\left(x\right)}\mathrm{sin}\left(x\right)\mathrm{cos}\left(x\right)}{\left(1+\mathrm{sin}\left(x\right){\right)}^{2}}.$By putting $t=\mathrm{sin}\left(x\right)$, it reduces to $\frac{t{e}^{t}}{\left(1+{t}^{2}\right)}$ but now I am not getting it. Jazmine Bruce 2022-05-22 Answered

### I'm currently stuck with a problem where I'm supposed to find all solutions that are asymptotic to the line $y=3-t$ when $t\to \mathrm{\infty }$. This is the demand, from here I'm supposed to create a first order linear differential equation. Can someone help me get started with this problem? Unsure of how to start....Asymptotic would mean that for example $x\left(t\right)=y\left(t\right)-1/t$ would satisfy the given demand, not sure how to go further with this although.A first order linear differential equation means I should have some sort of connection between my function and the derivative of the function, I cant make that connection....It's my first time using this forum so I've probably made every mistake you can make, hopefully my question is still relevant... qtbabe9876a9 2022-05-22 Answered

### What is the polar form of $\left(4,32\right)$ ? qtbabe9876a9 2022-05-22 Answered

### For $f\left(t\right)=\left(\mathrm{ln}t-{e}^{t},\frac{{t}^{2}}{{e}^{t}}\right)$ what is the distance between f(2) and f(4)?

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