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ind a salutien co the Inear equation 14x-y=-14
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- A=L+OEQUESTION 4 Consider the Black-Scholes-Merton formula: c = SoN(d₁) - Ke-™TN (d₂) p = Ke-TN(-d₂) - SoN(-d₁) where, d₁ = and d₂ = In(So/K)+(r+²)T αντ In(So/K)+(r)T αντ =d₁ - o√T a. Discuss the meaning of N(d₂).A:IV > partial derivative + V - L "dxdy Recall that for a general function fx), the integral feldx representa the difference of the area below the curve y = f(x) but above the r-axis when f(x) 2 0, and the area above the 104 CHAPTER 3. MULTIPLE INTEGRALS eurve but below the r-axis when f(x)s0. Similarly, the double integral of any continuous funetion f(x, y) represents the difference of the volume below the surface z=f(x, y) but above the xy-plane when f(x,y) 20, and the valume above the surface but below the xy-plane when flz,y) s0. Thus, our method of double integration by means of iterated integrals can be used to evaluate the double integral of any continuous funetion over a rectangle, regardless of whether fix, y)20 or not. Exumple 3.3. Evaluate [ sintx+ y)dxdy. Solution: Note that f(x,y)= sin(r+y) is both positive and negative over the rectangle [0,) (0,2n1 We can still evaluate the double integral: sin(x + yldzdy = (-conlx + y)dy (-cos(y+)+ cos y)dy - - sin(y+n)+ sin y. --sin3r…