3
lim =sqrt(9*x^6)/(x^3 + 8)
=3*x^3/(x^3 + 8)
=3*x^3/x^3
=3
Since 9*x^6 gets bigger much faster than x, the "-x" can be ignored under the square root. The square root of 9*x^6 is 3*x^3, since the square root of a power is dividing the power by 2. The x^3 gets bigger as 8 remains a constant, so the "+8" can be ignored. What's left is 3*x^3/x^3 = 3
lim =sqrt(9*x^6)/(x^3 + 8)
=3*x^3/(x^3 + 8)
=3*x^3/x^3
=3
Since 9*x^6 gets bigger much faster than x, the "-x" can be ignored under the square root. The square root of 9*x^6 is 3*x^3, since the square root of a power is dividing the power by 2. The x^3 gets bigger as 8 remains a constant, so the "+8" can be ignored. What's left is 3*x^3/x^3 = 3