find the differential dy. Hence, estimate the value of 1+ (1.023 2H y =

Q: Find div F and curl F if F(x,y, z) = 4y®z³i – 7x°z*j – 3xy°k. div F=|0 curl F=

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Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: Evaluate JJ xy dA , where R is the region in ху ´(1, 3) (5, 3) R (2, 1) (4, 1) A) 56 в) 67 38 D) 90

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: Find the length of the curve, L. y² = 4 (x + 5)* , 0 0

A: To find the length of the given curve

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Volume

Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: 1 Find the length of the arc of y= from x = 1 to x = 3. 2x

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Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: Find the gradient of the function at the given point. g(x, y) 11xe/x (13, 0) %3D Vg(13, 0) =

A: Gradient

Q: Show

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Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: Represent the plane curve by a vector-valued function

A:

Q: solution

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Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: 4. A commercial cattle company currently allows 20 steer per acre of grazing land. On average a…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: 27. | (u + 2)(u - 3) du 2+x 29.

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Q: Use the Babylonian's formula to calculate the circumference of a circle with diameter of 30 units.

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Q: Evaluate F. dr. F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - t*j, -2 sts 2

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: A torus formed by revolving the region bounded by the circle x2 + y2 = 49 about the line x = 8 (see…

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Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

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Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below:

Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

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Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: ... 3x+ 2y + 4z = 12 12 15

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Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: 2а-2х V4a-V4x

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Q: Find the area of the region using a double integral. The region bounded by y = 2x, x + y = 3, and…

A: To find the area of the region bounded by the given curves.

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

A:

Q: Sketch the region enclosed by the curves and find its area. cos 5x, y = 0, x = x = 10' 5 NOTE: Enter…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A:

Q: f' (x) = 3x* – 5x² + x

A:

Q: Use double integration to find the volume of the solid bounded by the paraboloid Z = 9x + y, below…

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Q: Find the area of the region enclosed by x² and y integrating with respect to y. the curves Y = 4x by…

A: A detailed solution is given below

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t = T .2. NG) = .2

A: