Multivariable Function Questions is Here

Recent questions in Multivariable functions

Arely Briggs 2022-01-25

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

kuntungw3 2022-01-24

Suppose that $x, y, z \in R$ with $a > 0$ a constant. Then, is the following true?
$f (x, y + c z, z) - f (x, y, z) = c \int_{0}^{1} (\partial_{x} + z \partial_{y}) f (x, y + θ z, z) d θ .$
It looks like the mean value theorem for multivariable function but I don't know why $\partial_{x}$ appears.

Zugdichte2r 2022-01-23

How do you find critical points for function of two variables $f (x, y) = 8 x^{3} + 144 x y + 8 y^{3}$ ?

GrareeCowui 2022-01-23

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

Nataly Best 2022-01-22

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 $n_{1}, n_{2} \in R$ given by
$Var (\hat{μ}) = \frac{σ^{2} (n_{1} + 2 n_{2})}{{(n_{1} + n_{2})}^{2}} .$
where $σ^{2}$ is a constant.
Can we say that $Var (\hat{μ}) \approx \frac{1}{n_{1} + n_{2}}$ and then conclude that $Var (\hat{μ}) \to 0$ as $n_{1} \to \infty$ and $n_{2} \to \infty$ ?
$lim_{(x, y) \to (\infty, \infty)} \frac{x + 2 y}{{(x + y)}^{2}}$
does not exist. Am I wrong to think of $Var (\hat{μ})$ as a function of two variables?

Vanessa Hensley 2022-01-22

How do you find critical points of multivariable function $f (x, y) = x^{3} + x y - y^{3}$

obrozenecy6 2022-01-07

I have the multivariable function
$\log (y^{2} + 4 x^{2} - 4)$
and I have found the maximal domain to be
$x^{2} + \frac{y^{2}}{4} > 1$

hvacwk 2022-01-07

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

Nicontio1 2022-01-07

Prove multivariable function is surjective
The function is $f : N^{2} \to N$ such that $f (a, b) = a^{b}$

Sam Longoria 2022-01-06

let x be a differentiable function $x : [a, b] \to R$ which satisfies:
$\frac{d x (t)}{d t} = f (t, x (t))$
$x (a) = x_{a}$
In particular I am trying to understand what $f (t, x (t))$ means, I understand this represents a multivariable function with parameters $t$ and $x (t)$ , but I can't think of what this would mean in the given context?

Kathleen Rausch 2022-01-05

Is it possible to graph out a multivariable function (3 variables at max) on a graphing calculator? If yes, how?

Walter Clyburn 2022-01-05

Differentiation of multivariable function proof
$\frac{d}{d x} \int_{v (x)}^{u (x)} f (t, x) d t = u^{'} (x) f (u (x), x) - v^{'} (x) f (v (x), x) + \int_{v (x)}^{u (x)} \frac{\partial}{\partial x} f (t, x) d t$

Donald Johnson 2022-01-04

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

garnentas3m 2022-01-04

Draw the gradient $\nabla f$ and level curves for $f (x, y) = x^{2} - y$ at a few common locations. For the point where the level curve $f (x, y) = 1$ meets the tangent line, write an equation $(\sqrt{2}, 1)$ .

Stefan Hendricks 2022-01-04

Derivative of a multivariable function
evaluate the derivative of a function $R \to R$ defined as
$g (t) = f (x + t (y - x))$
where $f : R^{n} \to R$ is a multivariable function and $x, y \in R^{n}$ . Prove that
$g' (t) = {(y - x)}^{T} \nabla f (x + t (y - x))$

pierdoodsu 2022-01-04

How do you define iterations of multivariable functions?
To be clear(example):
If $f : R^{2} \to R$
How do you define
$f \circ f, or f \circ \dots \circ f ?$ ?

Teddy Dillard 2022-01-04

How to find expressions for $f_{x x}$ and $f_{y y}$ for the multivariable function $f (x, y) = \ln (x^{2} y) + y^{3} x^{2}$ ?

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

Nicontio1 2021-12-11

Answer the following questions about an ANOVA analysis involving three samples.
a. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
b. State the null and alternate hypotheses for a three-sample ANOVA analysis.
c. What sample statistics must be known to conduct an ANOVA analysis?
d. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

Madeline Lott 2021-12-10

INVESTMENT ANALYSIS Paul Hunt is considering two business ventures. The anticipated returns (in thousands of dollars) of each venture are described by the following probability distributions:
$\begin{array}{cc} V e n t u r e A \\ E a r n i n g s & P r o b a b i l i t y \\ - 20 & 3 \\ 50 & 4 \\ 50 & 3 \end{array}$
$\begin{array}{cc} V e n t u r e B \\ E a r n i n g s & P r o b a b i l i t y \\ - 15 & 2 \\ 30 & 5 \\ 40 & 3 \end{array}$
a. Compute the mean and variance for each venture.
b. Which investment would provide Paul with the higher expected return (the greater mean)?
c. In which investment would the element of risk be less (that is, which probability distribution has the smaller variance)?

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.

Multivariable calculus

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