For  f ( x ) = e sin ⁡ ( x 2 ) {“version”:”1.1″,”math”:”f(x)=e^{\sin\left(\frac{x}{2}\right)}”} (a) Find the linearization of f(x) at x=0(b) Use the linearization to approximate the value of  e sin ⁡ 1 2 {“version”:”1.1″,”math”:”e^{\sin\frac{1}{2}}”} Note: Approximations done directly by plugging in the expression above in a calculator will not receive credit. Select an option from below:

Choose one of the following three optimization problems. Pay attention to the points. (a) For 8 points.The ideal dosage of a medication is a tradeoff between the efficacy of the drug and the severity of its side effects. If the side effects of a treatment are too severe, it will have to be discontinued, so it will fail to treat the patient. Similarly, if the dosage of the medicine is too low, its efficacy will not be sufficient to treat the patient. Suppose the probability of an effective treatment that accounts for this tradeoff is given by P(x), given below, where $x$ is the dosage of the medication given to the patient. What is the ideal dosage to maximize the cure?  P ( x ) = x 1 + x {“version”:”1.1″,”math”:”P(x)=\dfrac{\sqrt{x}}{1+x}”} (b) For 10 points.A box with an open top is to be constructed from a rectangular piece of cardboard (5 ft wide and 8 ft long) by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (c) For 12 points.An action movie character that loves to break the fourth wall is escaping from a mob of doppelgangers that want to take his place in the movie. He reaches a bank of a straight river, 3 km wide, with a boat unsuspiciously waiting for him. On the other side of the bank, 8 km downstream, he sees The Rock waving at him ready to fly a helicopter for their escape. At this moment he looks directly at the camera (at you) and asks “How can I move the fastest?” while getting himself on the boat. You know he can row at a speed of 6 km/hr and he can run at a speed of 8 km/hr. Should he go directly across (from A to C) and run the rest of the way (to B)? Should he row directly to the helicopter (from A to B)? or should he row for a bit (from A to D) and then run all that’s left to the helicopter? How long will it take him to reach the rock in the shortest time? He’s still staring at the camera, but the sound of the mob is getting louder, he’s counting on you! Select an option from below:

[FinA] In his study measuring spermatogenesis as the dependent variable, Dr. Friman utilized _______as the independent variable.

[FinA] Which of the following is not an example of challenging behavior typically associated with dementia?

[FinA] Renee recently moved into a group residential facility that provides treatment for dementia patients. Renee has stopped interacting with her caregivers and spends most of her time in bed. Which of the following challenging behaviors of dementia is Renee exhibiting?

[FinA] Which term is used by Trahan and Ripley as synonymous with “neurocognitive disorder”?

[FinA] Which of the following factors may contribute to a faster decline in neurocognitive functioning for someone with dementia?

[FinA] Cara researched the daily nutrients, food types, and water intake suitable for her body type. Each day, she records whether she consumed the daily intake requirement for each in her wellness journal. This would be an example of what type of behavior strategy?

[FinA] A runner tells her coach Miguel that she is aiming for a five-mile run without stopping by months end as she currently has to rest several times.  This is an example of:

[FinA] A major problem with the typical portrayal in the media of very young children as “Gerber babies” is that these images may: