98% 10:05 PM Sun Feb 27 webassign.net Need Help? Watch It Read It MY NOTES ASK YOU Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. x + x2 lim x- 0 5 - 4x2 Need Help? Read It
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- A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.Find the limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four decimal places.) lim x→7+ ln(x − 7)In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t=.0588s^1.125. where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1615 meters. t=____?
- In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t=.0588s^1.125 where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1602 meters. t= ____ secondsq3.1 Find the following limits analytically or state that they do not exist.. A ball is thrown vertically upward from the top of a building (when t=0seconds). It has a height function ?(?) = −???^2 + ??? + ???, where h(t) is in metres and “t” is in seconds. Use an appropriate limit where necessary.
- Let ƒ(x) = x^(1/(1-x)). a. Make tables of values of ƒ at values of x that approach c = 1 from above and below. Does ƒ appear to have a limit as x--> 1? If so, what is it? If not, why not? b. Support your conclusions in part (a) by graphing ƒ near c = 1To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modelled by the function C(t)= 40t/160+t,where C is the concentration, in grams per liter, and t is the time, in minutes. a) In how many minutes the saline concentration be 15 g/L?b) Is there an upper limit to the concentration in the tank? Explain. c) What restrictions must be placed on the domain of C if the tank has a maximum capacity of 150 000 L?A tank contains 1300 L of pure water. The solution that contains 0.01 Kg of sugar per liter enters the tank at the rate of 7L/min. and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the beginning? y(0)= to( Kg (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large what value is y(t) approaching? in other words, calculate the following limit lim t-oo y(t)= (kg)
- In the theory of relativity, the Lorentz contraction formula ______________L =L0 √ 1 - v2/c2 expresses the length L of an object as a function of itsvelocity with respect to an observer, where L0 is thelength of the object at rest and c is the speed of light. Find limv->c Land interpret the result. Why is a left-hand limitnecessary?The number s(t) of housing starts for single-family homes in the United States each year from 2006 through 2013 can be approximated by s(t)=500e.05(t-5)^2-100 where t is time in years since 2006. Numerically estimate limt+infinity s(t), and interpret the answerIn 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t = 0.0588 s 1.125 where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1604 meters. b. Find dt/ds when s = 60 and interpret the answer.