solve lim (5000t^2)/ (t+2)^2.

Question

the lim is t->infinity.

can someone show me the calculation. the ans is 5000.

Answer 1

limit ( 5000 t ^ 2) / ( t + 2 ) ^ 2 as t - > infinity =

5000 limit t ^ 2 / ( t + 2 ) ^ 2 as t - > infinity

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t ^ 2 / ( t + 2 ) ^ 2

when t = infinity = infinity / infinity

so you must use L'Hospital's rule

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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

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5000 limit [ d ( t ) / dt / d ( t + 2 ) / dt ] as t -> infinity =

5000 ( 1 / 1 ) = 5000