TheRedDevil18 said:By substituting 3 in the denominator, it would be undefined, so their is no limit ?
Vahsek said:Indeed, substituting 3 means that you would have 0 in the denominator, so the original expression would diverge as x → 3+. Therefore, you could argue that there is no limit since the expression would not converge to any real number per say.
That being said, I feel that a more precise answer is needed. For instance, you could say how it diverges.
TheRedDevil18 said:I'm guessing it would go to negative infinity then ?
A limit is a fundamental concept in mathematics that describes the behavior of a function as its input values approach a specific value. It is used to analyze the behavior of functions at points where they may not be defined or where they may have discontinuities.
To find the limit of a function, you need to evaluate the function as the input values approach the specific value in question. This can be done by plugging in values closer and closer to the specific value or by using algebraic techniques such as factoring, simplifying, and canceling out common factors.
The limit of the given function, lim x→3+ = 81-x4/(x2-6x+9)2, is equal to 81. This can be determined by plugging in values closer and closer to 3, which will result in the numerator approaching 81 and the denominator approaching 0. By simplifying the function, we can see that the limit is equal to 81.
Limits are important in mathematics because they allow us to analyze the behavior of functions at specific points, even if the function is not defined or has discontinuities at those points. They are also used in calculus to calculate derivatives and integrals, which are essential in many fields such as physics, engineering, and economics.
Yes, limits can be used to determine the continuity of a function. A function is continuous at a point if the limit of the function at that point exists and is equal to the value of the function at that point. If the limit does not exist or is not equal to the value of the function at that point, the function is said to have a discontinuity at that point.