Question

evaluate using l'Hopital's rule

lim x tends to 1[x^3-2x^2+x]/[x^5-1]

Answer 1

on top we have 3x^2-4x+1

on bottom we have 5x^4


the reason we can do f'/g' is because we have f(1)=0/g(1)=0

so we don't have than anymore

we can use direct substittion now

we have on top 3-4+1=0

on bottom we have 5*1=5

0/5=0 is the limit

Answer 2

3x^2-4x+1/5x^4 would be your new equation using l'Hoptial's rule

now plug in 1 to get
3(1)-4+1/5=0