If f=f(x, y), derive a forward finite difference approximation of 3rd order accuracy, O(h³), for ∂f/∂x.

Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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Q: | (sec 4x – 1)dx

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Q: (a) Evaluate the indefinite integral (anti-derivative) d.x Vr2 +1 by using the substitution u = x?…

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Q: When using a change of variables u = g(x) to evaluate the definiteintegral, how are the limits of…

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Q: Find the line integral of ƒ(x, y) = yex2 along the curve r(t) = 4t i - 3t j, -1 <_ t <_ 2.

A: Given: f(x,y)=yex2 r(t)=4ti-3tj -1≤t≤2 From r(t)=4ti-3tj x=4t,y=-3t Differentiate with respect to…

Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: Calculate the integral 0∫1xf′′(x)dx if f(0)=7, f(1)=2 and f′(1)=5, where f is a twice differentiable…

A: we have to find the following definite integral. For this we can use integration by parts

Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: Let f(x) = (x – 1)e* and h = 0.01. Calculate the %3D approximation to (a) f'(2.3) using second…

A: To calculate the approximation.

Q: By using the substitution method, show that for any positive numbers x and y ry 1 dt = Sdt

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: integral SS₁₁) dx dy xy=1, y = x, x=2 Calculate the in D limiteel to

A: An integral is a mathematical object that can be interpreted as an area or a generalization of an…

Q: The tangent function f (x) = tan x is integrable from 0 to T. O True O False

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Q: Evaluate the line integral [F-ds where F = 2xyi +(x-y³)j and C is (a) y =x from (0,0) to [10] (1,1)…

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Q: F(x) = sin(t) dt %3D 3x

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

A: Given xdy-ydx=4x4dx

Q: Show that the line integral is independent of path by finding a function f such that Vf = F. 2xe-Ydx…

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Q: Evaluate by Gauss divergence theorem for |] 4xz dy dz - y dz dx + yz dx dy S Sin tho a

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Q: Compute the line integral of the scalar function f(x,y) = sqrt(1 + 9xy) over the curve y = x^3 for…

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Q: Find the second-order Taylor approximation for f(x,y) = exp[-x]sin[y] at (2,0).

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: Suppose that f is integrable and that So f(z) dz = 3 and So f(2) dz = 7. Find %3D | f(2) dz b. f(t)…

A: Here given as ∫03fzdz=3 and ∫04fzdz=7 (a) Now  ∫04fzdz-∫03fzdz=∫34fzdz Thus ∫34fzdz=7-3=4

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: 2 10. F(s) : s+4 2s-10

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Q: Evaluate the line integral of the function p(x.y)=y-x,over the straight line Joining the two points…

A: Function p(x, y ) = y - x   points ( 4, 0 ) and ( 0, 4 )  To Evaluate: Integral  of the given…

Q: If F(z)dz f(t)dt, what are the bounds of integration for the first integral? and

A: Given  ∫abfxdx=∫−8−1fxdx+∫−11fxdx−∫−8−5ftdt

Q: Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(1, y) = In(r +y?) at…

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Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: If ƒ is continuous and f(t) dt = 16, find the integral

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Q: Set up an integral for the length of the curve. y = Vi-x7, -sxs 1/4 4+ 49, 12 dx -1/4 4- 4x7 + 7x6…

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Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: Let f(x) = (cosh x)² be defined on (0, 0), find %3D d 1/2) . dy

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Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: Find the total differential. z = x sin xy

A: Given: z=x sinxy To determine: The total differential of the given function.

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. X + dy

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Q: Find the limits of integration with respect to u and v

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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