The Essay Samples and Topic Ideas

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The mythical king of Thebes Introduction  When Oedipus grows he began to suspect his true origin and decides, he left the house, and on his way he ran into Layo who did not let him pass, and Oedipus kills him. Then, Oedipus manages to beat the Sphinx and becomes the new king of Thebes, and marries Yocasta, who in turn was his mother and Oedipus did not know.  Developing The people gathered to speak with Oedipus and ask for a solution to the weeds they were going through;Oedipus sent Creon to consult the oracle and he knew how to say that the people will be released from the weeds when they find and punish the murderer of Layo and Oedipus committed to the people to find the culprit....

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The characteristics of forests Introduction Thorny dry thicket. It is located in the driest and quality areas of the country, near the mangroves (Pacific Ocean) in the provinces of Guayas, Manabí, El Oro and Loja. The main characteristics of this forest to its elevation, since it is between 0 and 1000 m high, its vegetation ranges between 5-15 m, the species that inhabit these forests are spiny, with the presence of cactus and shrubs.  Decuuous dry forest. Also called as a very dry western forest, it is located in the provinces of Manabí, Guayas, El Oro and Loja at a height of 700 meters above sea.  Developing Being forests with warm climates, to keep water in times of drought loses 75% of...

The kidneys are excretory organs present in the body of vertebrate animals. Human beings have two kidneys whose shape resembles that of a bean. On the medial edge of each kidney is the hilum, where the ureter, the renal vein, the nerves and the artery passes. Wrapped by a fibrous fabric called renal capsule. Developing Around each kidney is a fatty fabric. Due to the presence of the liver. The kidneys are the adrenal glands are found. The kidneys have a reddish bean and brown coloration. They have approximately 12 centimeters and weigh up to 170 grams each. Anatomy and histology of the kidneys: the cortex to the renal marrow.  The renal cortex corresponds to the outermost layer, then the fibrous...

the departure of a patient, all the objects contained in the room, pillows, chairs, tables should be disinfected.  Hot or boiling water is a good method to eliminate germs, but you are not going to boil a table. The instruments or materials used to serve patients should be mostly disposable, to avoid the transmission of infections from one patient to another through injections needles and syringes should be disposable. It is very important that medications are not infected, if so, the medicine must be discarded and replaced by another that is not infected. But you're not going to boil a table. The instruments or materials used to serve patients should be mostly disposable, to avoid the transmission...

The points of inflections are (1, 1/√e) and (-1, 1/√e) b).f(x)=x+2sinxfirst derivative =1+2cos x Second derivative =2sinxGetting the local maxima and minima we equate the first derivative to zero 1+2cos x=0cos x=-12x=2π3, 4π3 evaluating the second derivative at x=2π3 and x=4π3-2sin2π3 =-2sin32=-√3. Therefore x=2π3 is a maximum value -2sin4π3 =-2sin-32=√3And x=4π3 minimum C. f(x)=x13(x+4)The first derivative =x13ddx(x+4)+x+4ddxx13=x13+(x+4)(13x23)=x13+(x3x23+43x23)f'(x)=43x23+4x133Using the product rule to get the second derivative =43ddxx-23+x13+x-23+x13ddx43=43(-23x-53+13x-23)f''x=-89x53+49x23d. The intervals on which the function increases or decreases and local...

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The length of a 12-foot by 8-foot rectangle is increasing at a rate of 3 feet per second and the width is decreasing at 2 feet per second (see figure below). How fast is the perimeter changing? Solution Given dl/dt=3 And dw/dt=-2 Then dp when l=12 ft and w=8ft Perimeter= 2l+2w Dp/dt=d/dt{2l+2w} =2dl/dt+2dw/dt=2(3)+2(-2) =2 ft/sec How fast is the area changing? Solution Given dl/dt=3, dw/dt=-2 Da/dt when l=12 ft , w=8ft Area=lxwDa/dt=d/dt{lxw} =Dl/dt*w+dw/dt*l =3(8)+ 12(-2) =0 ft2/sec (c) Find all critical points and local extremes of the following function on the given intervals. f (x) = 2-x3 on Solution To find the critical points, take...

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the function is given below Fill in the following table with approximate values (if they exist) 2 4 6 8 10 12 14 1 0 1 (b) For the function find and an equation of the tangent line to the graph of the above function at In the questions c to h , find (C ) y = x3 – x2 – x5/3 = 3x2 – 2x – 5/3x (d) y=x3 ln(1+x2) You may use (e) y'= 2+cosx+ ddxsinx-sinx. ddx(2+cosx)(2+cosx)2y'= 2+cosx.cosx-sinx. (-sin⁡(x))(2+cosx)2y'= 2+cosx+cos2 x+sin2(x)(2+cosx)2cos2 x+sin2x=1sin2x=1- cos2 xy'= 2+cosx+cos2 x+1- cos2 x(2+cosx)2y'= 1+ 2cosx(2+cosx)2(f) y=sin-1(ex)siny=(ex)cosyy'=(ex)y'=excosyy=ex1-e2x(g) Find if i.e. = ddxsin3(2x)=3sin22x.cos2x.2(2) (a) Find an equation...

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The expected value of the unhedged firm is: 0.5*200/(1+0.05)+0.5*(500-(500-300)*0.4)/(1+0.05)=95.24+200=295.24 Problem (b) Let’s buy put options for gold pricing at 500 with premium P. The expected value of the hedged firm is: (500-(500-300)*0.4)/(1+0.05)-P=420-P Problem (c) The safe debt is the one that pays off not more than 200 in a year. The value of the firm is:0.5*(200-200)/(1+0.05)+0.5*(500-200-(500-200-300)*0.4)/(1+0.05)=142.86 Problem (d) The safe debt is the one that pays off not more than 200 in a year. Let’s buy put options for gold pricing at 500 with premium P. The value of the firm is: (500-200-(500-200-300)*0.4)/(1+0.05)-P=285.71-P Problem (e) The firm’s value...

the function V (t, z) lim V( t, z ) / (t, z) = ∞ is said to is said to be decreasing in convex and in z if and only if V < 1. Q.3 V(t,x,y) = dXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dtdXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dt = stochastic differential equation let f(t, x, y) = logeXft = 0, fx = 1/x, fxx = -1/x2 df = 0 dt + ½ dx - 1/2x * 1/2 (dx)2 = 1/x (dXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dt) – 1/2x * ½ (2x2 dt) HJB = V( x,t,y) / t = ½ ydW2t + rXt –2 (V(x, t, y)/ x) + 2/2 * 2V(x, t, y) /...

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the time limit Such that Rearranginging Deviding by h Taking limits as h0 s.t The economic interpretation of g(t)y is labor income at the time, t. Part 2 2. 1. Optimal Trading Strategy Wealth process dXtπ=πtTμtdt+σtdWt+Xtπ-1nTπtX0=x0y=EβTI(βTST, where I is the optimal trading. where , and is uniquely determined by 2.2. Optimal Consumption in terms of X(t)+g(t)y= Such that,left952500 = Reference Bensoussan, A., & Zhang, Q. (2009). Mathematical modeling and numerical methods in finance. Amsterdam:...