 # Get help with multivariable calculus equations

Recent questions in Multivariable calculus

2022-02-11

### Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.  $F\left(x,y,z\right)={x}^{3}+cosyi+{y}^{3}sinxzj+{z}^{3}+2ek$ S is the surface of the solid bounded by the cylinder ${y}^{2}+{z}^{2}=4$ and the planes $x=0$ and $x=4$. Addison Gross 2022-01-25 Answered

### How do you find the critical point and determine whether it is a local maximum, local minimum, or neither for $f\left(x,y\right)={x}^{2}+4x+{y}^{2}$? Arely Briggs 2022-01-25 Answered

### I have the following multivariable function: $f\left(x,y\right)=x{y}^{2}$, and I must prove it is continuous at $\left(1,1\right)$. I have come to: $|{\left({\left(x-1\right)}^{2}+{\left(y-1\right)}^{2}\right)}^{\frac{3}{2}}-1|\le {\left({\left(x-1\right)}^{2}+{\left(y-1\right)}^{2}\right)}^{\frac{3}{2}}+1$ (Triangle inequality) $<{\delta }^{3}+1=ϵ$. What can I do with this 1? Any tips are welcome and thank you in advance! Ahmed Stewart 2022-01-25 Answered

### I have a multivariable function that is composed of six variables; four of these are constants ${C}_{1},{C}_{2},{C}_{3},{C}_{4}$ and the other two variables are x and y. The function is defined as follows $Xi\left(x,y,{C}_{1},{C}_{2},{C}_{3},{C}_{4}\right)$ I would like to find the maximum value of $Xi$ over $x\in \left\{-\mathrm{\infty },\mathrm{\infty }\right\}$ and $y\in \left\{-\mathrm{\infty },\mathrm{\infty }\right\}$. What is the rigorous mathematical notation I should use to describe this. Is this fine: $max\left\{Xi\left(x,y,{C}_{1},{C}_{2},{C}_{3},{C}_{4}\right)\right\}$ poveli1e 2022-01-25 Answered

### $f\left(x,y\right)=x\mathrm{sin}\left(x\right)+\mathrm{cos}\left(x\right)-y\mathrm{sin}\left(x\right)+\frac{{y}^{2}}{2}$My task is to find the critical points of this multivariable function (Determine the set of critical points of the function). Now I found the partial derivative to be${f}_{x}^{\prime }=\left(x-y\right)\mathrm{cos}\left(x\right)$${f}_{y}^{\prime }=y-\mathrm{sin}\left(x\right)$Wolfram Alpha says the critical point(s) is/are at $x=y$? How do I get the above in that form? The best I could do was get it in the form $x-y\mathrm{sec}\left(x\right)+\mathrm{tan}\left(x\right)=y$ Fallbasiss4 2022-01-25 Answered

### Write a multivariable function (i.e z=f(x,y)) for a linear function that contains the points (−1,0),(0,2),(1,−1). Ive kuntungw3 2022-01-24 Answered

### Suppose that $x,y,z\in \mathbb{R}$ with $a>0$ a constant. Then, is the following true?$f\left(x,y+cz,z\right)-f\left(x,y,z\right)=c{\int }_{0}^{1}\left({\partial }_{x}+z{\partial }_{y}\right)f\left(x,y+\theta z,z\right)d\theta .$It looks like the mean value theorem for multivariable function but I don't know why ${\partial }_{x}$ appears. GrareeCowui 2022-01-23 Answered

### Let S denote the solid enclosed by ${x}^{2}+{y}^{2}+{z}^{2}=2z$ and ${z}^{2}={x}^{2}+{y}^{2}$. What is the length of of the curve determined by (x,y,z): ${x}^{2}+{y}^{2}+{z}^{2}=2z$ and ${z}^{2}={x}^{2}+{y}^{2}$? What is the surface area of S? Zugdichte2r 2022-01-23 Answered

### How do you find critical points for function of two variables $f\left(x,y\right)=8{x}^{3}+144xy+8{y}^{3}$? Vanessa Hensley 2022-01-22 Answered

### How do you find critical points of multivariable function $f\left(x,y\right)={x}^{3}+xy-{y}^{3}$ Nataly Best 2022-01-22 Answered

### A quick question; is it possible to say in a way analogous to the single variable case that a multivariable function is "asymptotically equivalent" to a second multivariable function? For example, consider the function of ${n}_{1},{n}_{2}\in \mathbb{R}$ given by $\text{Var}\left(\stackrel{^}{\mu }\right)=\frac{{\sigma }^{2}\left({n}_{1}+2{n}_{2}\right)}{{\left({n}_{1}+{n}_{2}\right)}^{2}}.$ where ${\sigma }^{2}$ is a constant. Can we say that $\text{Var}\left(\stackrel{^}{\mu }\right)\approx \frac{1}{{n}_{1}+{n}_{2}}$ and then conclude that $\text{Var}\left(\stackrel{^}{\mu }\right)\to 0$ as ${n}_{1}\to \mathrm{\infty }$ and ${n}_{2}\to \mathrm{\infty }$? $\underset{\left(x,y\right)\to \left(\mathrm{\infty },\mathrm{\infty }\right)}{lim}\frac{x+2y}{{\left(x+y\right)}^{2}}$ does not exist. Am I wrong to think of $\text{Var}\left(\stackrel{^}{\mu }\right)$ as a function of two variables? reproacht3 2022-01-19 Answered

### Randomly drawing three green skittles in a row from a bag that contains eight green skittles out of 25 skittles total. deiteresfp 2022-01-18 Answered

### Find the conditional probability of the given event when two fair dice (one red and one green) are rolled. The red one is 6, given that the green one is 6. Miguel Reynolds 2022-01-18 Answered

### The ratio of the number of blue sticks to the number of green sticks in a box was 4:1. When David took out some blue and sticks and replaced them with an equal number of green sticks, the ratio of the number of blue sticks to the number of green sticks became 3:1. If there were 185 green sticks in the box now, (a) find the total number of blue and green sticks in the box, (b) find the number of green sticks in the box at first. sunshine022uv 2022-01-18 Answered

### There are 16 shirts in your closet, 6 blue and 10 green. You randomly select one to wear on Monday, do not return it to the closet, then select one to wear on Tuesday. What is the probability of wearing a blue shirt on Monday and a green shirt on Tuesday? William Boggs 2022-01-17 Answered

### A circular spinner is divided into 12 sectors of equal area: 5 red sectors, 4 blue, 2 yellow, and 1 green. In Problems 7–14, consider the experiment of spinning the spinner once. Find the probability that the spinner lands on: yellow or green? b2sonicxh 2022-01-17 Answered

### As Mark Ellon is getting ready for a meeting, the room goes dark. He fishes for a green shirt in his drawer. He wears only blue, green and white colors. His drawers have identical shirts in these colors: 28 blue, 25 green, and 13 white shirts. How many shirts did he throw on the floor to be a cent percent sure that he has a taken out a green shirt? eliaskidszs 2022-01-16 Answered

### Brad and Lena are recording their classmates' eye color for a statistics assignment. In Brad's class, 3 out of the 25 students have green eyes. In Lena's class, 2 out of the 20 students have green eyes. Which class has the greater ratio of green-eyed students to total students?

As you start exploring calculus and analysis, you will encounter multivariable calculus equations that are self-explanatory as well because all of them will contain at least two questions related to each variable being involved. See our multivariable calculus examples to receive more help and information regarding how these are used. The answers to solving these multivariable calculus questions should be based on finding the deterministic behavior. These are used in engineering and those fields where the parametric equations solver will provide you an optimal control of time dynamic systems. As an interesting subject, applying at least one equation in practice will keep you inspired!