lim -> infinity sqrt(x^2+3)
To find the limit of the function sqrt(x^2+3) as x approaches infinity, we can consider the behavior of the function as x gets larger and larger.
When x becomes very large, the term x^2 dominates the function. As a result, we can approximate sqrt(x^2+3) as sqrt(x^2) = x. This approximation becomes more accurate as x approaches infinity.
Therefore, the limit of sqrt(x^2+3) as x approaches infinity is infinity.
To find the limit of √(x^2 + 3) as x approaches infinity, we need to analyze the behavior of the function as x becomes larger and larger.
As x gets larger, the term x^2 dominates the expression x^2 + 3. This means that as x approaches infinity, the term 3 becomes negligible compared to x^2.
Therefore, we can simplify the expression:
lim(x -> infinity) √(x^2 + 3) = lim(x -> infinity) √(x^2) = lim(x -> infinity) x.
As x approaches infinity, the limit of x is also infinity.
So, the limit of √(x^2 + 3) as x approaches infinity is infinity.
To find the limit of √(x^2 + 3) as x approaches infinity, we can approach this problem using algebraic manipulation.
First, note that for large values of x, the term x^2 dominates the constant 3. Therefore, we can approximate the expression inside the square root as x^2, as x approaches infinity.
Now, we have:
lim(x -> ∞) √(x^2 + 3)
Using our approximation, we get:
lim(x -> ∞) √(x^2)
Simplifying further, we have:
lim(x -> ∞) x
Since x approaches infinity, the limit becomes infinity.
Therefore, the limit of √(x^2 + 3) as x approaches infinity is infinity.