I have one question about one of the problems in the book its number 20 in part 2.3
3x / cube root of [2+(4x^3)]
first thing i did was to 'kill' the cube root, so i tried by putting the numerator and denomitor to the power of 3 and then i got
27x^3 / 2+4x^3
then i divide both by x^3 getting
eventually i got 27/4 = 6.25 i did this same process for other questions and it worked well. but im not sure if this method is correct because in this question im getting a different answer(correct answer is 9/4)
Your first step is incorrect: when you raise the fraction to the power of three, you make an essential change to the original function, and so, to the original question.
Something does not seem right with either what I see as the statement of the question or with what you say is the correct answer. Your limit is limx -> infinity(3x)/CubeRoot(2+4x3), right? If yes, then the correct answer is 3/Cuberoot(4), and the easiest to get there is by factoring x3 inside the root and then taking the cube root of the two factors you get.