$MathMaster logo$

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

111 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 surface area of a rectangular solid if the length is 5 units, width is 3 units, and height is 4 units?

+

What is the value of sin(45°) divided by cos(60°) plus tan(30°)?

+

Find the equation of an ellipse centered at (h,k), major axis length 2a, and minor axis length 2b. (

+

New questions in Mathematics

90 divided by 40

What will be the density of a fluid whose volume is 130 cubic meters contains 16 technical units of mass? If required Consider g=10 m/s2

The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .

A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.

how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE

A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.

There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?

What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.

The simple average of 15 , 30 , 40 , and 45 is

7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see. H0 :x ̄<10hours HA : x ̄ > 13.5 hours

Sections of steel tube having an inside diameter of 9 inches, are filled with concrete to support the main floor girder in a building. If these posts are 12 feet long and there are 18 of them, how many cubic yards of concrete are required for the job?

List the remaining zeros of the polynomial with the given zeros Zeros are: 2, 3i, and 3 + i

36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt

factor the polynomial completely over the set of complex numbers b(x)=x^4-2x^3-17x^2+4x+30

Read the “Local Communities as Stakeholders: Does Amazon Really Need Tax Breaks?” example on p. 83 in Ch. 3 of Management: A Practical Introduction. In your response, discuss whether you feel that tax breaks for big companies benefit local communities. Describe ways to attract business to a region without having a negative impact on the larger community.

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

7-1=6 6x2=12 Explain that

A grain silo has a height of 8.8m with a 11.4m diameter. If it is filled 0.5% of it's volume, how much grain (m^3) is stored in the silo? (0 decimal places)