what is the Null Space o %3D a)= T,:R3_ R³ (T,x= xxa 03 义.a 13D Txlt)= x' (t) (Differen tiateon operator). %3D

Q: Compute fx + fxy + fyyzz, where f(x, y, z) = z sin(xy)

A: Given f(x,y,z)= z sin(xy)

Q: Theorem 6. Let X, Y be jointly continuous random variables. Then E[Y] = | E[Y|X = x] fx(x) dx %3D…

A:

Q: Show that every positve colufion at Ay + B, k=osl,2 bounded, %3D JK is i-e, osysB-if A<1. 1-A

A: Question: Objective is to find the upper bound of     yk+1=Ayk+B, k=0,1,2,... where yk is positive.

Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: nclude spaces in between 5. d te In (In y)) at y dy

A:

Q: TL (7,9) dydz = T" (17,19) dzdy. For any function f(r, y) continuous on the ry-plane, )True False…

A: To find- If the given statement is true or false.

Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

A:

Q: Verify that the integral of the beta density from −qto q equals 1 for(a) α = 2 and β = 4;(b) α = 3…

A: The Beta density function is given by: We need to prove:

Q: Find the local linearization of f(z) =z² at 9. lo(z) = %3D

A: Given : f(x) = x2   x0 =  9

Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

A:

Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: D (x) is not integrable on [0,1]

A: Note: Here we are solving 1st problem for the next problem please submit the question again. Given:…

Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

A: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

A:

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: + (xytl) Determine the Linearity of this DE. * ya dy y dy O Linear O Non-Linear

A:

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Let y = 4x2 + 7x + 4. If Az = 0.2 at z 4, use linear approximation to estimate Ay Ay s

A:

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

A:

Q: Show that f(x) = x² is integrable on [a,b].

A:

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: compute J secx dr. I n trying to integrate

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Q: f(~iy)= ve 1, fund warginal olistribution for 2. Fud conditimal pdf tos, s) o. Estmato (osyei / xo)…

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Q: Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

A:

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: Suppose that f and h are integrable and that: i fx) = -1, f(x) dx = 5, h (x) dx = 4 ,Find: a. S–2…

A:

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=3,…

A:

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: Evaluate the in tegral (x+ 2y) dy

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Q: find the volue of the od specify ingrol integrol T-x2 the

A:

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

A:

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

A:

Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

A:

Q: What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

A: Peanos theorem: "Consider the initial value problem y1= f(t,y), y(t0)=y0. Let f: Domain f →Rn. Then…

Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.