Hootenanny said:
Correctmoberry said:
Hootenanny said:Correct
The formula for calculating the limit of sqrt(x^2-9) is lim(x→∞) sqrt(x^2-9) = ∞.
To simplify the expression, you can first factor out the largest power of x in the square root, so the expression becomes lim(x→∞) x√(1-9/x^2). Then, you can apply the limit laws to simplify further.
No, the limit of sqrt(x^2-9) cannot be negative. As x approaches infinity, the value under the square root, x^2-9, will always be positive. Therefore, the limit will always be positive or infinite.
The expression sqrt(x^2-9) is significant in calculus because it represents the distance between a point (x,0) and the point (3,0) on the x-axis. It is also commonly used in finding the slope of a tangent line to a curve at a given point.
The value of x has a significant impact on the limit of sqrt(x^2-9). As x approaches infinity, the limit will also approach infinity. However, as x approaches -3 or 3 from either the left or right side, the limit will approach 0.