SOLUTION: Limits: Rational Function Q1)Let {{{f(x)=2x^8-12x^2+5}}} and {{{g(x)=c*x^n-4x^2+20}}} with {{{c<>0}}}. Then implies n = or > or < to ?. {{{lim(x->infinity, f(x)/g(x)=0)}}} Q

Algebra ->  Test -> SOLUTION: Limits: Rational Function Q1)Let {{{f(x)=2x^8-12x^2+5}}} and {{{g(x)=c*x^n-4x^2+20}}} with {{{c<>0}}}. Then implies n = or > or < to ?. {{{lim(x->infinity, f(x)/g(x)=0)}}} Q      Log On


   

Question 1037058: Limits: Rational Function
Q1)Let f%28x%29=2x%5E8-12x%5E2%2B5 and g%28x%29=c%2Ax%5En-4x%5E2%2B20 with c%3C%3E0. Then implies n = or > or < to ?.
lim%28x-%3Einfinity%2C+f%28x%29%2Fg%28x%29=0%29
Q2) Let 2x%5E6-12x%5E2%2B2 and g%28x%29=c%2Ax%5En-4x%5E2%2B15 with c%3E0. Then implies n = or > or < to ?.
lim%28x-%3Einfinity%2C+f%28x%29%2Fg%28x%29=infinity%29
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Limits: Rational Function 

Q1)  Let f%28x%29=2x%5E8-12x%5E2%2B5 and g%28x%29=c%2Ax%5En-4x%5E2%2B20 with c%3C%3E0. 

     Let   lim%28x-%3Einfinity%2C+f%28x%29%2Fg%28x%29=0%29.     <<<---  Then n > 8.  Independently on "c" (on the sign of "c").



Q2)   Let 2x%5E6-12x%5E2%2B2 and g%28x%29=c%2Ax%5En-4x%5E2%2B15 with c%3E0. 

      Let  lim%28x-%3Einfinity%2C+f%28x%29%2Fg%28x%29=infinity%29     <<<---  Then 3 <= n <= 5.