# Question #8da62

##### 1 Answer

First, divide both the numerator and denominator by

#lim_(x->-oo)(-2x^5 + x^4 - 3) / (3x^2-7)#

#lim_(x->-oo)(-2x^3 + x^2 - 3/x^2)/(3-7/x^2)#

The

#lim_(x->-oo)(-2x^3 + x^2)/3#

Now, we can prove that this limit equals

Since

#x^3# is an odd power, it will tend towards#-oo# as#x -> -oo# .

Therefore, multiplying#x^3# by a negative number will make it tend towards#+oo# .Therefore,

#-2x^3# will tend towards#+oo# as#x->-oo# .Since

#x^2# is an even power, it will tend towards#+oo# as#x -> -oo#

Since BOTH of the top terms will tend towards

#lim_(x->-oo)(-2x^3+x^2)/3 = +oo#

#therefore lim_(x->-oo)(-2x^5+x^4-3)/(3x^2-7) = +oo#