How do you find #lim (t^36t^2+4)/(2t^4+t^35)# as #t>oo#?
1 Answer
0
Explanation:
Finding the limit of a function is basically just a way to find out what value we get closer and closer to as we approach a certain number.
Finding the limit at infinity is no different. We should establish a couple of rules before we start.
Knowing this, we can go ahead and approach the problem as follows:
The first thing when taking the limit of a rational function is that we should focus our attention on the denominator. There, we must look at the highest power of the polynomial, which in our case is
#lim_(trarroo)(t^3  6t^2 + 4)/(2color(red)barult^4 + t^3  5)#
Next, we will take
#lim_(trarroo) ((t^3/color(red)[t^4]"6t"^2/color(red)[t^4]+4/color(red)[t^4]))/((("2t"^4)/color(red)[t^4]+t^3/color(red)[t^4]5/color(red)[t^4]))>lim_(trarroo) ((1/t6/t^2+4/t^4))/((2+1/t5/t^4))#
So, in our final step, we look at our rules that we noted above and simplify. Applying our rules, we get the following answer:

#lim_(trarroo)((stackrelcolor(blue)"0"cancel(1/t)stackrelcolor(blue)"0"cancel(6/t^2)+stackrelcolor(blue)"0"cancel(4/t^4)))/((2+stackrelcolor(blue)"0"cancel(1/t)stackrelcolor(blue)"0"cancel(5/t^4)))#
#color(white)(aaa)# 
#lim_(trarroo)(color(blue)0color(blue)0+color(blue)0)/(2+color(blue)0color(blue)0)#
#color(white)(aaa)# 
#lim_(trarroo)(0)/(2)#
#color(white)(aaa)# 
#color(magenta)[ 0#