Question

The limit as x approaches negative infinity is
(3x^5 + x + 2) / (8x^4 - 5)

a. DNE
b. 0
c. -3/8
d. 3/8

I think the answer is Choice C, but I was stuck between this answer and Choice D.

Answer 1

lim(3x^5 + x + 2) / (8x^4 - 5) , as x ---> negative infinity
divide top and bottom by x^4
= lim (3x + 1/x^3 + 2/x^4)/(8 - 5/x^4)
when x ---> - infinity, the terms 1/x^3, 2/x^4, -5/x^4 all approach zero, so we are left with

lim 3x/8 = lim (3/8)x
now as x ---> - negative, the result becomes - infinity

I don't know what DNE stands for, but none of the other choices are correct.

Answer 2

DNE means Does Not Exist, so (a) is the choice of choice.