$MathMaster logo$

MathMaster

Home
general
how to determine all points of a continuous function f x y sin x y x y limit tending to 1 if x y is different from 0 if x

Question

How to determine all points of a continuous function f (X,y)={sin(X+y)/X+y Limit tending to 1 If X+y is different from 0 If X+y =0

243

likes

1214 views

Answer to a math question How to determine all points of a continuous function f (X,y)={sin(X+y)/X+y Limit tending to 1 If X+y is different from 0 If X+y =0

$Expert avatar$

4.6

110 Answers

f(x,y) = \begin{cases} \frac{\sin(x+y)}{x+y}, & \text{if } x + y \neq 0 \\\lim_{t \to 1} \frac{\sin t}{t}, & \text{if } x + y = 0 \end{cases}

1. For points where

x + y \neq 0

, the function is given by

f(x,y) = \frac{\sin(x+y)}{x+y}

.

2. For points where

x + y = 0

, we evaluate the limit:

\lim_{t \to 1} \frac{\sin t}{t} = \frac{\sin 1}{1}

.

Therefore, the continuous function f(x,y) is

f(x,y) = \begin{cases} \frac{\sin(x+y)}{x+y}, & \text{if } x + y \neq 0 \\\frac{\sin 1}{1}, & \text{if } x + y = 0 \end{cases}

Frequently asked questions (FAQs)

What is the value of π/4 radians in degrees?

+

What are the components (x, y, z) of the unit vector in three-dimensional space?

+

What is 65% written as a decimal?

+

New questions in Mathematics

A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.

If you have a bag with 18 white balls and 2 black balls. What is the probability of drawing a white ball? And extracting a black one?

Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)

Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that

Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.

Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll? Draw the diagram

Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)

prove that if n odd integer then n^2+5 is even

-3(-4x+5)=-6(7x-8)+9-10x

A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9" and AD measures 56' - 3"

The blood types of individuals in society are as follows: A: 30%, B: 25%, AB: 20%, 0: 25%. It is known that the rates of contracting a certain disease according to blood groups are as follows: A: 7%, B: 6%, AB: 7%, 0: 4%. Accordingly, if a person selected by chance is known to have this disease, what is the probability of having blood group O?

Hola👋🏻 Toca en "Crear Nueva Tarea" para enviar tu problema de matemáticas. ¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!

Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.

Construct a set of six pieces of data with mean, median, and midrange of 67 and where no two pieces of data are the same.