Multivariable Calculus Examples: Learn Complex Calculus Problems

College
Calculus and Analysis
Multivariable calculus

Recent questions in Multivariable calculus

Sinead Mcgee 2021-09-06

Convert the equation into a first-order linear differential equation system with an appropriate transformation of variables.
$y " + 4 y^{'} + 3 y = x^{2}$

Khadija Wells 2021-09-06

The joint probability distribution of thr random variables X and Y is given below:
$f (x, y) = {\begin{cases} c x y & 0 < x < 2, 0 < y < x \\ 0 & other \end{cases}$
a.Find the value of the constant.
b.Calculate the covariance and the correlation of the X and Y random variables.
c. Calculate the expected value of the random variable $Z = 2 X - 3 Y + 2$

Ava-May Nelson 2021-09-06

Describe in general terms how to solve a system in three variables.

Rui Baldwin 2021-09-05

Combine variables for this equation
$f (x) = x^{2} + 7 x - 9$

Bevan Mcdonald 2021-09-05

Solve each equation over the set of complex numbers, find the magnitudes of the solutions and draw them in the complex plane. Hint: For some of the equations , to get n roots you must use $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ and $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$x^{3} + 1 = 0$

Kaycee Roche 2021-09-05

Exercise No. 10 (D.E. with coefficient linear in two variables)
Find the general / solution of the following D.E.
4. $(2 x + 3 y - 5) d x + (3 x - y - 2) d y = 0$

OlmekinjP 2021-09-05

Let $f (t) = t + i$ where $- π < t < π$ and has period $2 π$ . Why is it impossible to express the Fourier series of f(t) in real form?
A. Because f(t) is a complex function with $R e (f (x)) < 0$
B. Because f(t) is a complex function with $I m (f (x)) \neq 0$
C. Because f(t) is a complex function with $I m (f (x)) = 0$
D. Because f(t) is a complex function with $R e (f (x)) > 0$

BenoguigoliB 2021-09-05

Use the following linear regression equation to answer the questions.
$x_{1} = 1.3 + 3.0 x_{2} - 8.3 x_{3} + 1.6 x_{4}$
(a) Which variable is the response variable?
(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.
(c) If $x_{2} = 8, x_{3} = 2, and x_{4} = 6$ , what is the predicted value for $x_{1}$ ? (Use 1 decimal place)
(d) Explain how each coefficient can be thought of as a "slope" under certain conditions.

Tabansi 2021-09-05

Complex numbers can serve as entries in a matrix just as well as real numbers.Compute the expressions in Problems 51-53 , where
$A = [\begin{matrix} 1 + i & 2 i \\ 2 & 2 - 3 i \end{matrix}] and B = [\begin{matrix} 1 & - i \\ 2 i & 1 + i \end{matrix}]$
51.A+2B
52.AB
53. BA

Carol Gates 2021-09-05

Select the correct answer:
Which statement best describes the zeros of the function $h (x) = (x - 6) (x^{2} + 8 x + 16)$ ?
1. The function has two distinct real zeros
2. The function has three distinct real zeros.
3. The function has one real and two complex zeros.
4. The function has three complex zeros.

Tahmid Knox 2021-09-05

A polynomial P is given.
$P (x) = x^{3} + 216$
a)Find all zeros of P , real and complex.(Enter your answers as a comma-separated list. Enter your answers as a comma-separated list.)
x=?
b) Factor P completely.
P(z)=?

CMIIh 2021-09-04

A polynomial P is given.
$P (x) = x^{4} + 36 x^{2}$
Find all zeros of P , real and complex
a. $0, \pm 6 i$
b. $0, \pm 2 i$
c.0
d. $0, \pm 2$
e. $0, \pm 6$

Suman Cole 2021-09-04

Solve each problem and simplify it with no variables
$A = [\begin{matrix} a & - 2 \\ 1 & 3 \end{matrix}], B = [\begin{matrix} 4 & - 5 \\ b & 7 \end{matrix}]$
what is $A + B^{2}$ ?
What is $A^{2} - B$ ?

alesterp 2021-09-04

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
$f (x) = x^{4} - 5 x^{3} - 36 x^{2} + 272 x - 448$
All complex zeros are=?

pancha3 2021-09-04

Solve for G.S. / P.S. for the following differential equations using separation of variables.
$x^{2} y d y - x y^{2} d x + 3 y d y - 2 x d x = 0$

pancha3 2021-09-04

Solve the given differential equation by separation of variables.
$d y - (y - 8) 2 d x = 0$

aortiH 2021-09-04

(a)Show that for all complex numbers z and w
${| z - w |}^{2} + {| z + w |}^{2} = 2 {| z |}^{2} + 2 {| w |}^{2}$
(b) Let u,v be complex numbers such that $| u | = | v | = 1 and | u - v | = 2$ Use part (a) to express u in terms of v.

Nann 2021-09-03

Second derivatives For the following sets of variables, find all the relevant second derivatives. In all cases, first find general expressions for the second derivatives and then substitute variables at the last step.
$f (x, y) = x^{2} y - x y^{2},where x = s t and y = \frac{s}{t}$

Yasmin 2021-09-03

Let $X_{1}, X_{2}, \dot{s}, X_{n}$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that Pr $(X > 2000) \geq 0.95$

Kyran Hudson 2021-09-03

A polynomial P is given.
$P (x) = x^{4} - 16$
(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
x =?
(b) Factor P completely.
P(x) =?

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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