Multivariable Calculus Examples: Learn Complex Calculus Problems

College
Calculus and Analysis
Multivariable calculus

Recent questions in Multivariable calculus

arenceabigns 2021-09-15

3) Answer the following questions considering the complex functions given below.
a) Using the definition of complex derivative, evaluate f(z) expression using derivative operation based on limiting case as $lim_{△ z \to 0}$
a.1 $f (z) = \frac{1}{z^{2}}, (z \neq 0)$

Tyra 2021-09-15

Solve the system of equation by the method of your choice.
$x^{2} + {(y - 9)}^{2} = 49$
$x^{2} - 7 y = - 14$

Carol Gates 2021-09-15

Solve the given differential equation by separation of variables.
${(e^{y} + 1)}^{2} e^{- y} d x + {(e^{x} + 1)}^{6} e^{- x} d y = 0$

CMIIh 2021-09-15

Evaluate the integral by making an appropriate change of variables.

Kye 2021-09-15

Suppose X is a random variable such that $E (3 X - 7) = 8$ and $E (\frac{X^{2}}{2}) = 19$ .
What is Var $(70 - 2 X)$ ?

ddaeeric 2021-09-15

A supplement was given to patients to lower their blood pressure. The blood pressure before and after the supplement was recorded.
What kind of variables are Begin and End and what kind of scale are they following? Multiple choice. Choose one answer for scale and one answer for variables.
Note: the scale is identified as either nominal, ordinal, interval, or ratio (Choose the correct answer). Please explain why you chose the answer.
Variables are defined as either numerical (count/discrete or decimals) OR categorical (ordinal or nominal) (Choose the correct answer). Please explain why you chose the answer.

OlmekinjP 2021-09-15

Solve for i in terms of other variables:
$F = C [\frac{{(1 + i)}^{n} - 1}{i}]$

Annette Arroyo 2021-09-14

A salesperson earns $20 a day plus 10% commission on sales over $200. If her daily earnings are $25.40, how much money in merchandside did she sell?

CoormaBak9 2021-09-14

Solve the differential equation. (x and y are variables)
$(D^{2} + 4 D) y = 1 + 2 x + 3 x^{2}$

pancha3 2021-09-14

1. Given a complex valued function can be written as $f (z) = w = u (x, y) + i v (x, y)$ , where w is the real part of w and v is the imaginary part of v. Using algebraic manipulation figure out what wu and v is if
$f (z) = \overset{―}{z} (1 - e^{i (z + \overset{―}{z})})$
Here $\overset{―}{z}$ denotes the complex conjugate of z.
2. Using the concept of limits figure out what the second derivative of $f (z) = z (1 - z)$ is.
3. Use the theorems of Limits that have been discussed before to show that
$lim_{z \to 1 - i} [x + i (2 x + y)] = 1 + i . [Hint: Use z = x + i y]$

Brennan Flores 2021-09-13

Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of $100 + 100 \sqrt{3} i$

Trent Carpenter 2021-09-13

A polynomial P is given.
$P (x) = x^{3} + 64$
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.
$P (z) = ?$

Braxton Pugh 2021-09-13

Suppose that the random variables X and Y have the joint p.d.f.
$f (x, y) = {\begin{cases} k x (x - y), 0 < x < 2 & , - x < y < x \\ 0 & , elsewhere \end{cases}$
(i) Evaluate the constant k.
(ii) Find the marinal p.d.f. of the two random variables

snowlovelydayM 2021-09-13

Let $Y_{1}, Y_{2}, \dot{s}, Y_{n}$ be independent and identically distributed random variables such that for
$0 < p < 1, P (Y_{i} = 1) = p and P (Y_{i} = 0) = q = 1 - p$ (Such random variables are called Bernoulli random variables.)
(Maximum Likelihood Estimation ) Please construct the likelihood function for parameter p.
(Maximum Likelihood Estimation ) Please obtain the MLE estimator for p.

Marvin Mccormick 2021-09-13

In each of the following problems , use the information given to determine
a. $(f + g) (- 1)$
b. $(f - g) (- 1)$
c. $(f g) (- 1)$
d. $(\frac{f}{g}) (- 1)$
for the following functions,
$f = {(5, 2), (0, - 1), (- 1, 3), (- 2, 4)} and g = {(- 1, 3), (0, 5)}$
$f = {(3, 15), (2, - 1), (- 1, 1)} and g (x) = - 2$

Wotzdorfg 2021-09-12

Which of the following is true?
$\frac{d y}{d t} + \frac{y}{1 - t} = 3 t + 4$ is best solved with undetermined coefficients.
$\frac{d y}{d t} = \frac{t}{y - y t^{2}}$ is best solved with separation of variables.
$\frac{d y}{d t} = \frac{t}{y}$ is best solved with integrating factors.
$\frac{d y}{d t} = 2 y - \sin (5 t)$ is best solved with separation of variables.
$\frac{d y}{d t} = \frac{t}{y - y t^{2}}$ is best solved with undetermined coefficients.

snowlovelydayM 2021-09-12

Simplify $\frac{4 c + 16}{5 c} \div \frac{c + 4}{15 c^{3}}$ and state any restrictions on the variables.

York 2021-09-12

Plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians.
57. $1 - i$
58. $- 2 \sqrt{3} + 2 i$
59. $- 3 - 4 i$

Maiclubk 2021-09-12

Find the indefinite integral by making a change of variables.
$\int x^{2} \sqrt{1 - x} d x$

pedzenekO 2021-09-12

If z and $\overset{―}{z}$ are conjugate complex numbers , find two complex numbers, $z = z_{1} and z = z_{2}$ , that satisfy the equation $3 z \overset{―}{z} + 2 (z - \overset{―}{z}) = 39 + j 12$

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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