Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim (6x – In(x)) XStep 1 As x → [infinity], In(x) Step 2 Therefore, lim (6x - In(x)) is indeterminate of type [infinity] – [infinity] . We will change x → [infinity] it to a product by factoring out 4x to get lim x → [infinity] 6x 6x(1 - In(x)/6xStep 3 We now have lim x → [infinity] (6x − ln(x)) = lim x → [infinity] 6x 1 − ln(x) 6x. Let's first focus on lim x → [infinity] ln(x)/6x . Since ln(x) → [infinity] as x → [infinity], then this limit is indeterminate of type [infinity]/[infinity]. Using l'Hospital's Rule, we find: lim x → [infinity] ln(x)/6x = lim x → [infinity] 1/6x = 0Step 4 Since lim x → [infinity] In(x)/4x = 0, then we can conclude that: x → [infinity] lim (6x - In(x)) = lim 6x(1 - In(x)/6x)

If a boat travels 3 miles in 1.5 hours how far will it travel in 2 hours?

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

Joel wants to buy a new tablet computer fram a store having a 20% off sale on all tablets. the tablet he wants has an original cost of $190. he also wants to make sure he has enough money to pay the 5% sales tax. part one joel uses the incorect expression 0.95(190)(0.8) to calculate that the tablet will cost him a total of $144.40. describe his error and write the correct expression part two how much will joel pay for the tablet show your work if you answer this question correctly you will receive a prize of 99 points good luck