# Multivariable function questions and answers

Recent questions in Multivariable functions
Eve Dunn 2022-05-12 Answered

### How to solve for $a,b,c,d$ from two equations?Need to understand how to solve the following question:You have $50$ coins that add up to $1$ dollar. What are the possible combinations of pennys, nickels, dimes, and quarters that will satisfy these limits?$P+N+D+Q=50$$.01P+.05N+.10D+.25Q=1$

pettingyg0 2022-05-03 Answered

### Solve for w: 0=-7w+5x-3.

Davian Lawson 2022-05-03 Answered

2022-05-02

### use squeeze theorem find the following lim x,y-0,0 y^2(1-cos2x) /x^4 +y^2

Gage Potter 2022-05-02 Answered

### Solve for w in the equation y-1=4wy-6.

ngihlungeqtr 2022-05-02 Answered

### Solve for x: 0=-4u-7x+4.

dificultehcm 2022-05-01 Answered

### Solve for v in the equation -7=3uv+4.

Jordin Olsen 2022-05-01 Answered

### Solve for w: 0=-6u-7w-6.

Jordin Olsen 2022-05-01 Answered

### Solve for x in the equation 3-3x=w+1.

Dania Robbins 2022-04-30 Answered

### Solve for x in the equation a-7x+4=0.

Judith Warner 2022-04-30 Answered

### Solve for y: 0=u-5y+1.

broggesy9 2022-04-30 Answered

### Solve for x: 0=3u-7x-9.

habib A 2022-04-02

### Equation of the line tangent to $\left\{\begin{array}{l}y={x}^{2}\\ {z}^{2}=16-y\end{array}\right\$, at the point (4,16,0) ?a) $\left\{\begin{array}{l}4x=y\\ z=0\end{array}\right\$b)$\left\{\begin{array}{l}x=4\\ y=16\end{array}\right\$c)$\left\{\begin{array}{l}y-x=12\\ z=0\end{array}\right\$d)$\left\{\begin{array}{l}x+y=20\\ z=0\end{array}\right\$

2022-03-11 Answered

### Find the first and second derivatives of the function f(x) = x^2 ($\surd x-5$  )

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.

The multivariable function is related to regression analysis, which may be a bit challenging for college students as they implement estimation for the various data sets. Keeping all these challenges in mind, we aim to provide you with the answers to the most popular problems and questions where a helpful multivariable function example will be of help. You should also focus on each multivariable question by starting with analysis and proper calculation of each variable as you exchange various practical sets. The purpose is to remove the constraints of single variables as you add any calculations.