Question

4x^3+6x^2-2/3x^2-4x+5 lim x>>>00

Answer 1

What is the main problem for you?

Answer 2

When you have a fraction and a limit, you must look at the highest power. In this case, the highest power is x^3.

x^3 is going to dominate the rest of the lower powers and determine the limit. The coefficient in this case and the rest of the powers will not matter.

Since x^3 is on the top of the fraction, the top will grow at a rate much higher than the bottom of the fraction.

Therefore, as x approaches infinity, the top of the fraction will be much larger than the bottom. As x grows larger, so does the fraction.

Hence, as x approaches infinity, the fraction approaches infinity.