Whats the limit of e^(3x) / x^2 as x approaches infinity?

Answer 1

Since this is an indeterminate case, you can use L'Hopital's Rule. (Take the derivative of the top over the derivative of the bottom)
So you get: Lim of 3e^(3x)/2x as x goes to infinity. Since this still equals infinity over infinity, take the derivatives again.
Now: Lim of 9e^(3x)/2. Now you can substitute in infinity and your answer is infinity!

Hope that helped.

Answer 2

TA is genuine in any respect cases ;) once you plug in x=0 you get [0/0] it is an indeterminate. prepare L'Hop rule: lim x => 0 (2x) / -sinx ===>nevertheless [0/0] repeat L'Hop lim x=> 0 (2) / -cosx ===> hence 2/(-a million) = -a million answer = -2 also, you would possibly want to understand lim x=>0 of sinx / x = x /sinx each and every ==> 0 in case you do no longer understand L'Hopital's rule, then multiply the numerator and denominator by technique of the conjugate: (x^2) / (cosx -a million) multiply excellent/bottom by (cosx +a million) x^2 (cosx + a million) / (cos^2(x) - a million) ====> use Pyth identity sin^2x+cos^2x=a million =x^2(cosx + a million) / -sin^2(x) = - ( x/sinx )( x/sinx ) (cosx + a million) each and every sinx / x reduce is going to at least one as x is going to 0 hence = - (cos x + a million) = -(cos0 + a million) = -(a million+a million) = -2 :)

Answer 3

Would there technilay be no limit as if one side is as you say approcahing infinity or pretty much allready there which both means the same. then the equation would also have no limit.

Cheers
Michael H Flack

Answer 4

answer is infinity

use L 'Hospital's rule or

expand e^3x as power series and divide each term by x^2
then take limit

Answer 5

Unbounded growth growth to infinity. x is in the exponential in the numerator, and as x increases, although the denominator will increase very quickly, the numerator will overtake it, driving the value to infinity.

Answer 6

E=mc2

Answer 7

infinity

exponential functions grow faster than any power function; therefore e^(3x) wins out over x^2.

Answer 8

Yo Mama.

Answer 9

wich infinity,postive or negative?
if it's positive so the limit is positive infinity
and if it's negative so there's no limit

Answer 10

Use your differential calculus.. Makes it 3/2X... then 3 = 2X, then X = 3/2..