x* – 1 f. lim x-1 x In x sin 3x g. lim x-0

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

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Q: n2-2

A: Question number 5 is solved step by step. Solving more than 1 question is against the policy of…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: 324-y' y dx dy 18

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Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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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: 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: Find the curvature and the radius of curvature at the point t = 0. %3D x = e' cos(t), y = e' sin(t),…

A: r(t)=et cos(t) i+et sin(t) j+7et kr'(t)=[etcost-etsin(t)] i          +[etsint+etcos(t)] j +7et k…

Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

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

A: We have to calculate volume of solid obtained by revolving the region enclosed by curves x=cosecy,…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

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Q: r = V cos 20 r = 5 cos 0

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Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: xe*y dy dx

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Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x' and…

A: Solution:

Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10+ 10 sin…

A:

Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

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Q: [r(t)xu(t)] , in two dilferent ways Find CHE).t)] and rt)- costi + sintj +tk, u(t)=j+Ek dt (i) Find…

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Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: Evaluate J xy dA¸ where Ris the region in y =x? 2 A 13/7 16/3 18 D) 20 B.

A: To find : ∬xydA where  R is the region of y=x2 and y=0

Q: rl+ 4sino

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Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) Find the…

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Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

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: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy : -54 -36

A: Triple integral

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

A: Given

Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

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Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 3.

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Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: Solving

Q: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

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Q: d Calculate ri(t) · r2(t)] and d dt [r1(t) x r2(t)] first by differentiating dt the product directly…

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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: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

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Q: Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your…

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: Given:          Curve y=2x2+10                     y=4x+16

Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

A: