For each of the following functions, determine whether they are  ODD, EVEN or NEITHER. Justify your answer algebraically. NO graphs! f 1 ( x ) = cos ⁡ ( x 4 + x ) {“version”:”1.1″,”math”:”f_1(x)=\cos(x^4+x)”} f 2 ( x ) = sin ⁡ ( x 5 ) x {“version”:”1.1″,”math”:”f_2(x)=\dfrac{\sin(x^5)}x”} f 3 ( x ) = sin ⁡ ( π 2 + x ) {“version”:”1.1″,”math”:”f_3(x)=\sin\biggl(\frac\pi 2+x\biggr)”} f 4 ( x ) = e x + e − x e x − e − x {“version”:”1.1″,”math”:”f_4(x)=\dfrac{e^x+e^{-x}}{e^x-e^{-x}}”} f 5 ( x ) = x − ⌊ x ⌋ − 1 2 ,   x ≠ 0 , ± 1 , ± 2 , ± 3 , … , {“version”:”1.1″,”math”:”f_5(x)=x -\big\lfloor x \big\rfloor – \frac 12,\ x\ne 0, \pm 1, \pm 2, \pm 3,\ldots,”} where  ⌊ x ⌋ = def the largest integer less than or equal to  x {“version”:”1.1″,”math”:”\text{where } \big\lfloor x \big\rfloor\overset{\text{def}}=\text{the largest integer less than or equal to } x “}

Find the Fourier series of the 2π{“version”:”1.1″,”math”:”2π”}-periodic function q(x)=1-sin3(2x).{“version”:”1.1″,”math”:”q(x)=1-sin3(2x).”}

A 9-month-old infant has had a fever of 103°F for 2 days and now has a diffuse, non-pruritic, maculopapular rash that blanches on pressure. The infant’s immunizations are up-to-date. What is the most likely diagnosis?

Which of the following statements is true regarding the mode of disease transmission?

Which of the following statements regarding febrile seizures in children is true?

What standard diagnostic test is considered the “gold standard” in diagnosing Multiple Sclerosis?

Kelsie, age 11 years, has been inattentive at school.  Her mother says she is always fidgety, easily distracted, and forgetful.  Kelsie’s teacher suggested she should be evaluated for Attention-Deficiency Hyperactivity Disorder. Which screening tool should the nurse practitioner  use? 

Which of the following laboratory findings is most indicative of an infection?

Jennifer, age 5 years, is a new patient at the clinic.  During the visit, her mother states Jennifer was diagnosed with fever of unknown origin 3 months ago by their previous healthcare provider.  She denies fevers for the past month.  The nurse practitioner knows which of the following is a common cause of fever of unknown origin in children?

The nurse practitioner is counseling an adolescent who was recently hospitalized for an asthma exacerbation and learns that the child usually forgets to use twice- daily inhaled corticosteroid medications that are supposed to be given at 0800 and 2000 each day. Which strategy may be useful in this case to improve adherence?