Why stochastic integral could be defined like So g(s) dw(s) = lim (b gn(s) dw(s) (W) (026 n->

Q: Suppose h(x)= e*g(x). Find h '(0) given that g(0) = 9, g ' (0) = 7. h' (0) = %3D

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Q: D. f(x) = In x + 2e - 3x2

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Q: If a population is distributed normally with mean 0 and standard deviation 1, then the probability…

A: Given function is f(x)=e-x22 Solution for part a:…

Q: If f(2) = 1, f'(2) = 2, g(2) = 2 and g' (2) = 1, then f(x) g(z) %3D %3D %3D

A: Given : f2=1f'2=2g2=2g'2=1

Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

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Q: 5 If f(2) = 3, f(5) = 7, f' (2) = 5, f' (5) = 3, and f"() is continuous, then what is

A: To evaluate: ∫25xf''(x)dx Use integration by parts here. First, find

Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: Let f(x) = sinh(2x) then f'(In2) = %3D %3D

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Q: If f(0) = 1, ƒ'(0) = -1. g(0) = –1, g (0) = –3, and h(x) = (x² + f(x))g(x) then h' (0) =... O -2 O 2…

A: Given: f0=1, f'0=-1, g0=-1, g'0=-3 and hx=x2+fxgx. To find: h'0 Solution: Product rule of…

Q: If f(1) = -5.4, f'(x) is continuous, and f'(x)dx = 20, what is the value of f(4)?

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Q: apital stock C and net investment I are related by: (image 1) Identity (1) shows the synonymity…

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Please help

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Q: If F(x) f(g(x)), where f(1) = 8, f '(1) = 3, f '(-1) = 5, g(-1) = 1, and g'(-1) = 4, find F '(-1).…

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Q: dy Find dx if y = x (log2(x* – 4x))° dy dx ||

A: Topic = Derivative

Q: An epidemic spreads through a population at a rate proportional to the product of the number of…

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Q: 19. (E x' 3) dx

A: #19 Differentiation w.r.t. x

Q: 1. Find dy dx S(x)= e**/2x-5 (6-5x)* (iii) f(x) =

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Q: Suppose f(2) = 1, f'(2) = –6, and | dH H(x) = (1 + f(x))³. Find dx Н (2) %3

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Q: you know f(t) = L¯'{F(s)}, how would you find {F(s)/s²j? %3D

A: Inverse Laplace transform

Q: 4. If f(0) = g(0) = 0 and f" and g" are continuous, show that %3D f(x)g"(x) dx = f (a)g'(a) –…

A: Given that f(0)=g(0)=0 and f" and g" are continuous. To show that      ∫0af(x) g"(x)…

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

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Q: If f(x) = then ƒ"(x)= = x S² (t³ + 4t 0 (t³ + 4t² + 6) dt SI

A: given,  f(x)=∫0x(t3+4t2+6)dtwe know→(i)  ∫xndx=xn+1n+1+c(ii)  d dx(xn)=nxn-1(iii)  d dx(constant)=0

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: If f(1) = 4, f'(1) = 2 and g(x) = lInf(e*), then g'(0) is : %3D %3D %3D А. О в. O C. 2 С.2 D. 1 18…

A: Given: if f1=4, f'1=2 and gx=lnfex To Find: g'0 Concept: (i). Chain Rule for…

Q: Suppose that f(1) = 4, f(4) = 5, f'(1) = 4, f'(4) = 4, and f" is continuous. Find the value of…

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Q: 20/40) ty' + (t + 1)y = t, y(ln 2) = 1, t >0

A: Given, ty'+(t+1)y=t And initial condition y(ln2)=1

Q: Find initial value of X(s) = 10 (s+1)/(s+2)(s+6

A: Given function is, Xs=10s+1s+2s+6 As, we know that from the initial value theorem for xs,…

Q: - While working with a colleague you encounter the following initial value problem: dy (2² – 9) -…

A: From the Peano's theorem,