math
posted by ifi .
solve lim (5000t^2)/ (t+2)^2.
the lim is t>infinity.
can someone show me the calculation. the ans is 5000.

limit ( 5000 t ^ 2) / ( t + 2 ) ^ 2 as t  > infinity =
5000 limit t ^ 2 / ( t + 2 ) ^ 2 as t  > infinity
________________________________________
t ^ 2 / ( t + 2 ) ^ 2
when t = infinity = infinity / infinity
so you must use L'Hospital's rule
________________________________________
5000 limit t ^ 2 / ( t + 2 ) ^ 2 as t  > infinity =
5000 limit [ d ( t ^ 2 / dt ) / d ( t + 2 ) ^ 2 / dt ] as t > infinity =
5000 limit [ t / ( t + 2 ) ] as t > infinity
________________________________________
5000 limit [ d ( t ) / dt / d ( t + 2 ) / dt ] as t > infinity =
5000 ( 1 / 1 ) = 5000