Question 3 > Evaluate the definite integral psin(?) cos(r)dr = Submit Question\f. Question 12 Evaluate the limit using L'Hospital's rule ex - 1 lim sin(2x) Question Help: Video Submit Question. Question 5 Suppose you deposit $4000 at 9% interest compounded continously. Find the average value of your account during the first 3 years. Question Help: Video Submit QuestionQuestion 7 A bacteria culture starts with 680 bacteria and grows at a rate proportional to its size. After 6 hours there will be 4080 bacteria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be the population after 5 hours? (c) How long will it take for the population to reach 2670? Submit Question\f. Question I5 ? If a cup of coffee has temperature BET in a room where the ambient air temperature is ETC, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is TH] = 23 + 553 H5\". 1What is the average temperature of the coffee during the first 10 minutes? average temp =| |=C Question Help: [E] V": eo Question 15 Use L'Hospital to determine the following limit. Use exact values. lim r Inc Submit QuestionQuestion 8 Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the dT differential equation dt = k(T - A), where T is the temperature of the object after t units of time have passed, A is the ambient temperature of the object's surroundings, and & is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 64 degrees for 12 minutes, the coffee reaches 174 degrees. How long will it take before the coffee reaches 157 degrees? Include at least 2 decimal places in your answer. minutes Submit QuestionQuestion 4 Evaluate the indefinite integral. 3es sin(es) dx = Submit