Show that the following functions are harmonic, that is, that they satisfy Laplace’s equation, and find for each a function f ( z ) of which the given function is the real part. Show that the function v ( x , y ) (which you find) also satisfies Laplace’s equation. 3 x 2 y − y 3
Show that the following functions are harmonic, that is, that they satisfy Laplace’s equation, and find for each a function f ( z ) of which the given function is the real part. Show that the function v ( x , y ) (which you find) also satisfies Laplace’s equation. 3 x 2 y − y 3
Show that the following functions are harmonic, that is, that they satisfy Laplace’s equation, and find for each a function
f
(
z
)
of which the given function is the real part. Show that the function
v
(
x
,
y
)
(which you find) also satisfies Laplace’s equation.
5. Determine the derivative of the following complex functions:
a. f(z) = (z³ + 3z²)³at z = 2i
b. Item 5b at at z = 4i
The position function of a particle is given by ?(?) , where t is measured issecond and s is measured in metres.
a) Find the velocity and acceleration functions.
b) When does the particle change direction?c) What is the velocity at ? = 3 seconds? Is the particle moving away or towards its starting position?
Find an equation for the line tangent to the following curve at the point (2, 1).
1 – y = sin (x + y – 3)
-
Use symbolic notation and fractions where needed. Express the equation of the tangent line in terms of y and x.
equation:
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY