The limit of x/sqrt(x^2 + 1) as x approaches positive infinity is equal to 1. This means that as x gets larger and larger, the value of the expression gets closer and closer to 1.
To calculate the limit of x/sqrt(x^2 + 1) as x approaches positive infinity, we can use the limit definition and substitute infinity for x in the expression. This will give us the limit value of 1.
Finding the limit of x/sqrt(x^2 + 1) as x approaches positive infinity is important because it helps us understand the behavior of the expression at large values of x. It also allows us to make predictions and analyze the function's behavior in this limit.
No, the limit of x/sqrt(x^2 + 1) as x approaches positive infinity is not equal to infinity. As x gets larger, the value of the expression approaches 1, not infinity. This means that the function has a horizontal asymptote at y=1, but it does not approach infinity.
Yes, the limit of x/sqrt(x^2 + 1) as x approaches positive infinity can be evaluated using L'Hopital's rule. By taking the derivative of the numerator and denominator separately and substituting infinity for x, we can still get the limit value of 1.