14. What is a common cause of forgetting information over time?

16. What does chunking help with?

20. Sensory memory retains information for several minutes.

13. Which type of amnesia involves difficulty in forming new memories after an injury?

Solve the quadratic equation  

Valerie is making a corral with 700 feet of fencing.  She is making a rectangular corral and then using two lines of fencing to divide it into three equally sized rectangular pens. (See image).  What dimensions should the corral have in order to maximize the total area of the Corrals?  

Find the Horizontal or Oblique Asymptote  

Existence-Uniqueness Theorem: If f(x, y) and df/dy are continuous on a rectangle R in the xy-plane containing the initial condition y(x0)=y0, then the initial value problem y’=f(x,y), y(x0)=y0 has a unique solution in R. 6pts Determine whether the Existence-Uniqueness Theorem can be used to determine if the initial value problem: y’ = 1/x + y1/3,    (1,1)  has a unique solution.  Please indicate the largest possible rectangle R from the Theorem.   21pts First order ODEs: Solve the following. Provide solutions in explicit form if possible. Theorem: M(x,y) dx + N(x,y) dy = 0 is an exact equation if dM/dy = dN/dx. a.  (y4 + 1)cos x dx – y3 dy = 0 b.  (12x – y)dx – 3x dy = 0 c.  (x3 + y/x)dx + (y2 + ln x) dy = 0   8pts Homogeneous ODE: Solve y iv + 5y ‘’ – 36y = 0.   10pts Nonhomogeneous ODEs: Solve the following with either undetermined coefficients or variation of parameters to solve  3y ‘’ – y’ – 2y = 4x + 1, y(0) = 1 and y’(0) = 0   10pts Systems: Solve the following.                   x1’ = 2×1 – 4×2                                      x2’ = 2×1 – 2×2   15pts Solve the initial value problem for y(t) using the method of Laplace transforms. y ’’ + 4y’ + 3y = 1 y(0)=0,   y’(0) = 0   Taylor polynomial about 0: pn(x) = f(0) + f’(0)x + f ‘’(0)/2! x2 + f ‘’’(0)/3! x3 +  … + f (n)(0)/n! xn   15pts Determine the first three nonzero terms in the Taylor polynomial approximations for the given initial value problem y ’’ – 2y’ + y = 0;          y(0)=0,   y’(0) = 1   Theorem: Consider the differential equation A(x) y” + B(x) y’ + C(x) y = 0.  If the functions p(x) = B(x)/A(x) and q(x) = C(x)/A(x) are analytic at x =0, then the general solution is produced by the power series centered at x=0: y(x) = a0 + a1x + a2 x2 + a3 x3 + …   15pts Determine the first four nonzero terms in the power series expansion about x=0 for a general solution in the given ODE y ’’ + xy’ + y = 0           

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One of the hallmark laboratory findings in hypoadrenocorticism is