I think that your first steps would be to graph y = [[x]] and y = [[-x]], and then graph y = [[x]] + [[-x]].CrossFit415 said:lim x --> n ([[x]] + [[-x]]) where n is an integer and [[ ]] is the greatest-integer function.
How would I go on about this?
Would I have to plug in n for x? So i got ([[n]] + [[-n]])
Limit problems are mathematical problems that involve finding the value that a function approaches as its input approaches a certain value. They are important to master because they are a fundamental concept in calculus and are used to solve a variety of real-world problems in fields such as physics, engineering, and economics.
The main difference between a limit problem and a regular algebraic problem is that in a limit problem, the input value is approaching a specific value, while in a regular algebraic problem, the input value can be any value. In addition, limit problems involve the use of calculus concepts such as derivatives and integrals, while regular algebraic problems do not.
When solving a limit problem involving the absolute value of x, it is helpful to split the problem into two separate cases: when x is positive and when x is negative. This allows you to use the definition of absolute value to simplify the problem and find the limit.
One expert tip for solving limit problems is to always start by plugging in the given value for the input and see if it leads to a definitive answer. If not, try to simplify the problem by factoring, canceling out common terms, or using trigonometric identities. It is also important to understand the properties of limits, such as the sum, product, and quotient rules, to make the problem easier to solve.
To check your answer for a limit problem, you can use a graphing calculator or an online limit calculator to graph the function and see if your answer aligns with the graph. Additionally, you can use algebraic techniques to simplify your answer and see if it matches the simplified form of the function. Finally, you can also use the definition of a limit to verify your answer by plugging in the given input value and seeing if it leads to the same result.