Find the limit of the function algebraically.

limit as x approaches zero of quantity x squared plus three divided by x to the fourth power.

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Adoctor administers a drug to a 38-kg patient, using a dosage formula of 50 mg/kg/day. assume that the drug is available in a 100 mg per 5 ml suspension or in 500 mg tablets. a. how many tablets should a 38-kg patient take every four hours? b. the suspension with a drop factor of 10 ggt/ml delivers the drug intravenously to the patient over a twelve-hour period. what flow rate should be used in units of ggt/hr? a. the patient should take nothing pills every four hours. (type an integer or decimal rounded to the nearest hundredth as needed.)

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3