JG89 said:Factor out a sqrt(x^2) from the numerator.
KevinL said:I don't believe you can just do that. Only if two things are multiplied beneath a radical can something be taken out.
Multiplying by x/x does not help either.
Hmm, perhaps you can say that as x gets arbitrarily large, its sqrt(3x^2)/x because the 1 becomes meaningless and thus the limit is sqrt(3)?
The limit of this function as x approaches infinity is infinity.
To find the limit, we can use the fact that as x gets larger and larger, the term with the highest power (x^2) dominates the other terms. Therefore, we can ignore the 1 in the numerator and the x in the denominator, and the limit becomes the same as the limit of sqrt(3x^2)/x. Simplifying this further, we get the limit as x approaches infinity of sqrt(3), which is infinity.
No, the limit is not an indeterminate form. Indeterminate forms occur when the limit cannot be determined by simple algebraic manipulation, but in this case, we can determine the limit by simplifying the expression.
Yes, we can use L'Hopital's rule to find the limit. By taking the derivative of the numerator and denominator, we get the limit as x approaches infinity of (3x)/sqrt(1+3x^2). As x approaches infinity, the denominator becomes larger and larger, causing the limit to approach infinity.
The value of the limit remains the same regardless of the constant multiplied to the function. This is because, as x approaches infinity, the constant becomes insignificant compared to the term with the highest power (x^2).