 Recent questions in Multivariable functions Nicontio1 2022-01-07 Answered

Prove multivariable function is surjective The function is $$\displaystyle{f}:\mathbb{N}^{{2}}\rightarrow\mathbb{N}$$ such that $$\displaystyle{f{{\left({a},{b}\right)}}}={a}^{{b}}$$ hvacwk 2022-01-07 Answered

multivariable functions works when the partial derivatives are continous but if the function is just differentiable does the chain rule work ? I mean if $$\displaystyle{z}={f{{\left({x},{y}\right)}}}$$ is differentiable function and $$\displaystyle{x}={g{{\left({t}\right)}}},{y}={h}{\left({t}\right)}$$ are also differentiable functions can we write: $$\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{t}\right.}}}}={\frac{{\partial{f}}}{{\partial{x}}}}\times{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}+{\frac{{\partial{f}}}{{\partial{y}}}}\times{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}$$ obrozenecy6 2022-01-07 Answered

I have the multivariable function $$\displaystyle{\log{{\left({y}^{{2}}+{4}{x}^{{2}}-{4}\right)}}}$$ and I have found the maximal domain to be $$\displaystyle{x}^{{2}}+{\frac{{{y}^{{2}}}}{{{4}}}}{>}{1}$$ Sam Longoria 2022-01-06 Answered

let x be a differentiable function $$\displaystyle{x}:{\left[{a},{b}\right]}\rightarrow{R}$$ which satisfies: $$\displaystyle{\frac{{{\left.{d}{x}\right.}{\left({t}\right)}}}{{{\left.{d}{t}\right.}}}}={f{{\left({t},{x}{\left({t}\right)}\right)}}}$$ $$\displaystyle{x}{\left({a}\right)}={x}_{{a}}$$ In particular I am trying to understand what $$\displaystyle{f{{\left({t},{x}{\left({t}\right)}\right)}}}$$ means, I understand this represents a multivariable function with parameters $$\displaystyle{t}$$ and $$\displaystyle{x}{\left({t}\right)}$$, but I can't think of what this would mean in the given context? Walter Clyburn 2022-01-05 Answered

Differentiation of multivariable function proof $$\displaystyle{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\int_{{{v}{\left({x}\right)}}}^{{{u}{\left({x}\right)}}}}{f{{\left({t},{x}\right)}}}{\left.{d}{t}\right.}={u}'{\left({x}\right)}{f{{\left({u}{\left({x}\right)},{x}\right)}}}-{v}'{\left({x}\right)}{f{{\left({v}{\left({x}\right)},{x}\right)}}}+{\int_{{{v}{\left({x}\right)}}}^{{{u}{\left({x}\right)}}}}{\frac{{\partial}}{{\partial{x}}}}{f{{\left({t},{x}\right)}}}{\left.{d}{t}\right.}$$ Kathleen Rausch 2022-01-05 Answered

Is it possible to graph out a multivariable function (3 variables at max) on a graphing calculator? If yes, how? garnentas3m 2022-01-04 Answered

Sketch the level curves for $$\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}-{y}$$ together with the gradient $$\displaystyle\nabla{f}$$ at a few typical points. Write an equation for the tangent line of the level curve $$\displaystyle{f{{\left({x},{y}\right)}}}={1}$$ at the point $$\displaystyle{\left(\sqrt{{{2}}},{1}\right)}$$. Stefan Hendricks 2022-01-04 Answered

Derivative of a multivariable function evaluate the derivative of a function $$\displaystyle\mathbb{R}\rightarrow\mathbb{R}$$ defined as $$\displaystyle{g{{\left({t}\right)}}}={f{{\left({x}+{t}{\left({y}−{x}\right)}\right)}}}$$ where $$\displaystyle{f}:\mathbb{R}^{{n}}\rightarrow\mathbb{R}$$ is a multivariable function and $$\displaystyle{x},{y}\in\mathbb{R}^{{n}}$$. Prove that $$\displaystyle{g}′{\left({t}\right)}={\left({y}−{x}\right)}^{{T}}\nabla{f{{\left({x}+{t}{\left({y}−{x}\right)}\right)}}}$$ Donald Johnson 2022-01-04 Answered

First of all, I'm new to multivariable calculus... in a multivariable function, by assuming that its domain is going to be $$\displaystyle{R}^{{2}}$$ and its image is going to be all real numbers, the graph of that function is defined as a subset of $$\displaystyle{R}^{{3}}$$ in which the x and y axis are going to receive the inputs, and the output is going to be in $$\displaystyle{z}{\left({x},{y},{f{{\left({x},{y}\right)}}}\right)}$$ ? Is that correct? Will its graph, in this example, be some kind of surface? pierdoodsu 2022-01-04 Answered

How do you define iterations of multivariable functions? To be clear(example): If $$\displaystyle{f}:\mathbb{R}^{{2}}\rightarrow\mathbb{R}$$ How do you define $$\displaystyle{f}\circ{f},\text{or}{f}\circ\ldots\circ{f}?$$? Teddy Dillard 2022-01-04 Answered

How to find expressions for $$\displaystyle{f}_{{{x}{x}}}$$ and $$\displaystyle{f}_{{{y}{y}}}$$ for the multivariable function $$\displaystyle{f{{\left({x},{y}\right)}}}={\ln{{\left({x}^{{2}}{y}\right)}}}+{y}^{{3}}{x}^{{2}}$$? Sho 2021-12-13

Consider the following statement of masses, If both masses start from rest, A) find a1?   B) find a2 ?   C) How fast is m1 moving after sliding the 2.00 m shown? *Assume both masses are simultaneously released from the rest*  vetrila10 2021-11-20 Answered

Contract analysis. A contractor's financial outlay X and labor force Y are random variables with bivariate pdf given by: $$\displaystyle{{f}_{{{X},{Y}}}{\left({x},{y}\right)}}={k}{x}{y}$$ for $$\displaystyle{10},{000}{<}{x}{<}{100},{000}$$ and $$\displaystyle{10}{<}{y}{<}{20}$$ and $$\displaystyle={0}$$, elsewhere. (a) Evaluate constant k. (b) Detemine the marginal pdf of X and Y. hexacordoK 2021-09-19 Answered

Prove mathematically (using variables, not numbers) that kx>kz for hydraulic conductivity - topic: Groundwater Hydrology $$\displaystyle{K}_{{z}}={\frac{{{d}}}{{{\frac{{{d}_{{1}}}}{{{K}_{{1}}}}}+{\frac{{{d}_{{2}}}}{{{K}_{{2}}}}}+\dot{{s}}+{\frac{{{d}_{{n}}}}{{{K}_{{n}}}}}}}}$$ $$\displaystyle{K}_{{x}}={\frac{{{K}_{{1}}{d}_{{1}}+{K}_{{2}}{d}_{{2}}+\dot{{s}}+{K}_{{n}}{d}_{{n}}}}{{{d}}}}$$ he298c 2021-09-19 Answered

Find the Jacobian of the transformation $$\displaystyle{x}={u}+{4}{v},{y}={u}^{{2}}-{2}{v}$$ melodykap 2021-09-18 Answered

Describe the procedure for finding critical points of a function in two independent variables. Wribreeminsl 2021-09-18 Answered

Question No.3, Part (A) i. From the Euler Relatins, decude that $$\displaystyle{e}^{{-{3}{i}{\frac{{\pi}}{{{4}}}}}}=-{\frac{{\sqrt{{2}}}}{{{2}}}}{\left({1}+{i}\right)}$$ ii. Find the cartesian form of the complex number , $$\displaystyle\sqrt{{2}}{e}^{{{i}{\frac{{\pi}}{{{4}}}}}}$$ iii. Find polar and exponential forms of the complex number , $$\displaystyle{\frac{{{3}}}{{{2}}}}+{\frac{{{3}\sqrt{{3}}}}{{{2}}}}{i}$$ CoormaBak9 2021-09-17 Answered

There are four washing machines in an apartment complex: A, B, C, D. On any given day the probability that these machines break down is as follows: P(A) = 0.04, P(B) = 0.01, P(C) = 0.06, P(D) = 0.01 . Assume that the functionality of each machine is independent of that of others. What is the probability that on a given day at least one machine will be working? Chaya Galloway 2021-09-17 Answered

Explain how to find the degree of a polynomial in two variables. Tazmin Horton 2021-09-17 Answered

Convert the equalities below equalities by adding sack variables. Use $$\displaystyle{s}_{{1}}\ \text{ and }\ {s}_{{2}}$$ for your slack variables. $$\displaystyle{3}{x}_{{1}}+{9}{x}_{{2}}\leq{42}$$ converts to () =42 $$\displaystyle{15}{x}_{{1}}+{7}{x}_{{2}}\leq{38}$$ converts to () = 38

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.
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