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icosane
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Homework Statement
Lim as x goes to infinity of sqrt(x^2 + 1) / x
The Attempt at a Solution
know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?
A limit problem is a type of mathematical problem that involves finding the value that a function approaches as its input (x) gets closer and closer to a specific number or infinity.
The most common method for solving a limit problem is to use algebraic techniques such as factoring, simplifying, and combining like terms. Another approach is to use the properties of limits, such as the limit laws, to manipulate the expression and find the limit value.
This notation indicates that we are trying to find the limit of a function as the input (x) approaches infinity. In other words, we are looking at the behavior of the function as the value of x gets larger and larger without bound.
The limit as x goes to infinity of sqrt(x^2 + 1) / x is equal to 1. This can be determined by factoring out an x from the numerator and denominator, which simplifies the expression to sqrt(1 + 1/x^2). As x approaches infinity, 1/x^2 becomes smaller and smaller and approaches 0, making the entire expression equal to 1.
Solving limit problems is important because it allows us to understand the behavior of a function as its input approaches a specific value. This can help us make predictions about the behavior of the function, evaluate the continuity of a function, and find the derivatives of functions, which are essential in many mathematical and scientific applications.