#3) Determine whether the funchon 2XZ72 iS onto if; @ flmin)= mtn © f(mm) =m-D O f(m, n) = Ini @ f(min)= m²4n2

Q: Sketch the Part of tthe slope Field of y'=L for X and y be tween -5 and 5. Then add to your sketch…

A: Slope field of y' =1/y

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Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: Let f,g:[a, b]-X are Riemann integrable , f-g is Riemann integrable.

A: Let f,g:a,b→R are Riemann integrable.To prove that f-g is Riemann integrable.

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: 2. Calculate the divergence of D = (÷)[10xyzảy + 5x²zãy + (2z3 – 5x²y)ã,] at P(-2,3,5).

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Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

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Q: sho w that fQ) = x xE To,1] is Riemann integrable amm

A: The given function is: fx=x3, x∈0,1

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Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: 3. Show that the divergence of a curl is zero.

A: according to our guidelines we can answer only one question and rest can be reposted

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A: Given query is to find the derivative of function T.

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A: To find: Differential equation of circle with centre 2,k and radius r. We know that equation of…

Q: (15) Find the divergence and curl of i = (ryz)î + (3x²y)ĵ + (æz² – y²z)& at point (2, –1,1).

A: Given v→=xyzi^+3x2yj^+xz2−y2k^ We have to find the divergence and curl of v→ at point 2,−1,1. If…

Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: (m) Suppoe that a >0 and that f is Riemann integrable on [-a, a). If f is even slow that (b) Let /…

A: According to the given information, For part (a) Suppose that a>0 and that f is Riemann integral…

Q: Every function which is Riemann 0/3 integrable on [a,b] is continuous. * True O False

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Q: Let R = [0, 1] × [0, 1] . Estimate ſfr 6(x + y) dA by computing two different Riemann sums, %3D

A: Given, R=0,1×0,1 and ∫∫R6x+ydA let us assume that fx,y=6x,y. Here, we required to calculate Riemann…

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Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: If f: [a, b] - R is bounded and has only a finit number of discontinuous points, then f is Riemann…

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Q: 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by 2.x2 f…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

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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: Eualuate Hhe suface intearml SS Fids for Hie gulen. Vactor field F and the onented suorice S. In…

A: For the solution follow the next steps.

Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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

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Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

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Q: Show that if f is Riemann integrable on [a,b] and f(x) ≥ 0 for all x ∈ [a,b], then

A: A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is…

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…

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Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

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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…

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Q: 11. Show that the definite integral of f(x) = c over [a, b] is c(b-a) by applying the definition of…

A: Here given function as fx=c where the function fx is defined on the interval a, b.

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A: Given

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A: We have to find work done.

Q: Let f,g:[a, b]-R are Riemann integrable , f-g is Riemann integrable.

A: True Statement

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

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Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.