Multivariable Calculus Examples: Learn Complex Calculus Problems

College
Calculus and Analysis
Multivariable calculus

Recent questions in Multivariable calculus

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
$g' (t) = {(y - x)}^{T} \nabla f (x + t (y - x))$

David Lewis 2021-12-17

A camera shop stocks eight different types of batteries, one of which is type A7b.Assume there are at least 30 batteries.
of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b.
How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must
include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight
different types of the inventory includes at most three A7b batteries

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)?

lunnatican4 2021-12-09

For each of the following test, outline a research scenario and use any hypothetical data to show how the test is conducted
i. Analysis of variance
ii. Chi-square for goodness-of-fit test
iii. Chi-square test for independence

kuvitia9f 2021-12-08

On the final examination in Engineering Data Analysis, the mean was 72 and the standard deviation was 15.
1. Determine the standard scores (z-values) of students receiving the grade of 65.
2. Determine the standard scores (z-values) of students receiving the grade of 85

Shelia Lawrence 2021-12-08

A geologist has collected 15 specimens of basaltic rock and 15 specimens of granite. The geologist instructs a laboratory assistant to randomly select 25 of specimens for analysis.
a) What is the pmf of the number of granite specimens selected for analysis? (Round your probabilities to four decimal places.)
$\begin{array}{cc} x \\ p (x) \end{array}$
b) What is the probability that all specimens of the two types of rock are selected for analysis? (Round your answer to four decimal places.)
c) What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (Round your answer to four decimal places.)

rastafarral6 2021-12-02

$\int_{1}^{0} \tan (x^{2}) d x + 2 \int_{1}^{0} x^{2} \sec^{2} (x^{2}) d x = \frac{π}{4}$
Select one:
True
False

Eichowa4 2021-11-26

Graph the equation $x^{2} + y^{2} + 4 x - 6 y - 3 = 0$ in a rectangular coordinate system. If two functions are indicated, graph both in the same system.Then use your graphs to identify the relation’s domain and range.

philosphy111of 2021-11-26

Solve the polynomial inequality
$x^{2} - 2 x + 1 > 0$
and graph the solution set on a real number line. Express the solution set in interval notation.

Halkadvalseln 2021-11-23

The function $f (x) = 2 x^{3} - 33 x^{2} + 168 x + 9$ has one local minimum and one local maximum.
Use a graph of the function to estimate these local extrema.
This function has a local minimum at $x = ?$
with output value:
and a local maximum at $x = ?$
with output value:

vousetmoiec 2021-11-23

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
$\frac{π}{4} \leq θ \leq \frac{3 π}{4}, 0 \leq r \leq 1$

Mahagnazk 2021-11-23

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results $y = 3 x^{\frac{2}{3}} - 2 x$

tbbfiladelfia6l 2021-11-23

The Munchies Cereal Company combines a number of components to create a cereal. Oats and rice, two of the constituents, offer vitamins A and B. The business is trying to determine how much oats and rice, in terms of ounces, should go into each box of cereal in order to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while keeping costs as low as possible. In comparison to rice, which provides 6 milligrams of A and 2 milligrams of B per ounce, oats provide 8 milligrams of A and 1 milligram of B. Oats cost $0.05 per ounce and rice cost $0.03 per ounce.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
c. What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?

Virginia Caron 2021-11-22

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
$θ = \frac{2 π}{3}, r \leq - 2$

deliredejoker7m 2021-11-22

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
$- \frac{π}{2} \leq θ \leq \frac{π}{2}, 1 \leq r \leq 2$

ambiguit 2021-11-22

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
$r \geq 1$

Sheelmgal1p 2021-11-22

A commodity has a demand function modeled by $p = 126 - 0.5 x$ and a total cost function modeled by $C = 50 x + 39.75$ , where x is the number of units.
(a)Use the first marginal analysis criterion presented in class to find the production level that yields a maximum profit. Then use the second criterion to ensure that level yields a maximum and not a minimum. Finally, what unit price (in dollars) yields a maximum profit?
$ per unit
(b)When the profit is maximized, what is the average total cost (in dollars) per unit? (Round your answer to two decimal places.)
$ per unit

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!

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