No, not at all. You'll have terms with x + 1 and x - 1 to the 1/3 and 2/3 powers. For each of these terms factor as x(1 + 1/x). Depending on the power the original terms are raised to, you'll pull out a factor of x^(1/3) or x^(2/3). In the end, you'll have x to the same power in the numerator as in the denominator, so they cancel.sara_87 said:so, that means we have to use the binomial expansion inorder to divide by x^1/3 ??
The limit as x tends to infinity is a mathematical concept that represents the behavior of a function as the input value (x) approaches infinity. It is denoted as lim f(x) as x approaches infinity and is used to determine the value that a function approaches as its input value grows without bound.
The limit as x tends to infinity is calculated by evaluating the function at increasingly larger values of x. As x gets closer and closer to infinity, the output value of the function will approach a specific value. This value is the limit as x tends to infinity.
If the limit as x tends to infinity does not exist, it means that the function does not approach a specific value as x gets larger and larger. This could be due to the function oscillating between different values or approaching different values from different directions.
The limit as x tends to infinity has many applications in physics, engineering, and economics. It is used to model the behavior of systems such as population growth, radioactive decay, and fluid flow. It is also used to analyze the stability and convergence of numerical algorithms.
The limit as x tends to infinity is used to describe the behavior of a function as its input value approaches infinity. It is not the same as infinity itself, but rather a way to describe how a function behaves as it approaches infinity. In some cases, the limit as x tends to infinity may approach infinity, but this is not always the case.