Please help! Problem 4. (i) Verify thatS(S.t) = (ar+3o")(r-ngsis a solution of the Black-Scholes partial differential equation1with f(0, t) - 0 for 0SIST and f(Sr.T) S;(i) Consider a derivative with underlying asset whose price S follows the Ito processds - uSdt + aSdB and which provides a single payoff at time T > 0 in theamount of S, where Sr is the underlying asset price at time T. What is theprice of this derivative at time 0

Given that fS,t=e2r+3σ2T-tS3 1 we have to verify that equation (1) is…

Answered: Problem 4. (i) Verify that is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Mid Term Exam 1s.. > Wasit University Subject mathermatics Engineering college Time: 2 hours Mechanical Eng. Department Class: 1 vear M.Sc Abdalameer Alrubaiee Date: 7/ 3 /2021 Mid Term Exam 2020-2021 First Semester Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative. Q2 find the derivative of the following: 1) y = 2sin (5x) ,2) y = Inxncosh 5x ,3) xsin-14y = y tan-14x 4) v = ecosh-(8x) 5) v = t +1 and x = Vt +1 Q3 Find dy/dx on the graph y sec/x2 + y? = cos2x at point (1, 2). Good luck Msc. Abdalameer Airubalee
(4) This exercise is intended to be an initial exposure for taking derivatives with a different variable other than r. The same rules apply, just use the given variable instead of r. (y? + 8)* (a) If f(y) = find f'(y). (b) If z = 9t?e-4", find (c) If k(8) = In (64 + 0), find [k(8)].
1 , the first four derivatives evaluated at a = 4 are: For the function f(x)= V2x+1 -1 -,f(a)= 2.33 1.3 .f"(a) = 22.35' -1-3-5 (a) = f(a)=. f"(a)- 1.3.5-7 23.37 24.39 -1 f(a)=글.fa)-r"a)=그:3·5"(a)-1:3.5.7 39 1.3 ,f"(a) = -1.3.5 f"(a)3D 37 33 35 -1 1.3 ,f"(a) -1.3.5 33 35 37 1 f(a) =,f'(a) = "(a) = -1 1.3 -1.3-5 ,f(a): 2.3 (a) = 24.37 %3D 22.33* 23.35 QUESTION 10 1 Using your answer from Problem 9, what is fn(a) for f(x): at a = 4 for n 2 li %3D
1.2 Find first derivative 2 for the following functions. dx (a) ]y = 5+ 6x + 4x3 (b) |y = In(2x) + x (c) dy= (2x² + 3x)(5x – 1) (d) y = e3x+2x² (e) y = In MacBook Pro 80 000 000 DII DD F3 F4 F5 F6 F7 F8 F9
1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her y' = h'(x)e-4f(x) + h(x)e-4f(x) (-4) work. After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method.
33) In Problems 33) through 35), given MB ' (x) =HD(x), HD' (x) = PR (x) , PR' (x) = RB(x) with the vaules : MB(x) HD(x) PR(x) RB(x) - 2 - 4 3 3 9. 14 12 7 Find the value of the 3nd derivative of MB(x) at x = 3, MB '' '(x) Ix = 3=. A) 5 B) 7 C) 12 D) 14 34) J RB(x)dx =, A) MB(x) + C B) HD(x) + C C) PR(x) + C D) MB ' (x) 35) Find the AREA under the curve of y = HD(x) over [ - 2, 3], A = . Ay y = HD(x) A = ? A) 12 B) 13 C) 14 D) 17
1. Find the third order derivative f""(2) of f(x) = x³. Of" (2) = 1 Of"" (2) = 0 Of"" (2) = 12 Of"" (2) = 6 OIt does not exist
Set up the appropriate form of a particular solution yp of the dif-ferential equation y''''-y''-2y'+2y =xe^(x)+x^(2)cosx
5
1) find the derivative of y = 4x2 – 3x – 2 %3D then evaluate f'(x+3)
Example 2: Approximate the derivative of y=x´ at x=1 by forming small changes Solution :- JADY) = 5(x+AX)² +3(x+AXJ +=5(+2XDメ+泌+38 4り25メー+10XDX+5DX-2 y(1) = (1)° = 1 y(1.01) = (1.01)² =1.0201 Ay = 1.0201–1=0.0201 y+y =(5x x3X)+ DX (10 dy Ay 0.0201 = 2.01 Dy z D X\OX+5XAX dx Ar 0.01
3x²y' = x(5-6y) x = 1; y = 2

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Problem 4. (i) Verify that is a solution of the Black-Scholes partial differential equation Si+rSfs+5o*s®fss = rf 1