what is the horizontal limits of :
(10x^3-11x^2-2x)/(7-8x^3)
To find the horizontal limits of a function, we need to determine the behavior of the function as x approaches positive infinity and negative infinity.
For the given function:
f(x) = (10x^3 - 11x^2 - 2x) / (7 - 8x^3)
As x approaches positive infinity, the highest power of x dominates the expression. In this case, the highest power of x is x^3. So, as x approaches positive infinity, the function behaves like:
f(x) ≈ (10x^3) / (-8x^3)
The x^3 terms will cancel out, leaving:
f(x) ≈ -10 / 8
Therefore, as x approaches positive infinity, the value of the function approaches -10/8 or -1.25.
Similarly, as x approaches negative infinity, the highest power of x dominates the expression. In this case, the highest power of x is x^3. So, as x approaches negative infinity, the function behaves like:
f(x) ≈ (10x^3) / (-8x^3)
Again, the x^3 terms cancel out, leaving:
f(x) ≈ -10 / 8
Therefore, as x approaches negative infinity, the value of the function approaches -10/8 or -1.25.
Hence, the horizontal limit of the function is -1.25 as x approaches either positive or negative infinity.