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Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. %3D If u(1, — 3) — 7, и, (1, —…

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Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

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A: Given that,   Using integration by part

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Q: Find div F and curl F if F(x, y, z) = x*i – 11j + yzk. div F= curl F=

A: Vector

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A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: S cos³ 3x dx

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Q: Use a truth table to determine whether the two statements are equivalent. (p v q) a r and p v (q A…

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Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

Q: Find div F and curl F if F(x, Y, z) = 11y°z°i – 3x*z°j – 6xy°k. - div F= curl F=

A: The given vector function is: F(x,y,z)=11y6z5i-3x4z6j-6xy3k Let, F(x,y,z)=F1i+F2j+F3k then…

Q: xdx 46. S- V3+2x². – x+

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Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: Differentiate the following using implicit differentiation 3/a + V = 7

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Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: Use series to evaluate the limit. X-In(1 +x) lim

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Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt' the product directly and…

A: r1(t)=cos⁡(t)i+sin⁡(t)j+6tk,r2(t)=5i+tk Given:  ddtr1(t)⋅r2(t)=r1(t)⋅dr2dt+dr1dt⋅r2(t) and…

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Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: Please

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Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 4.…

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Q: Find curl (3zi + 4xj+ 5yk). curl(3z i+ 4xj+ 5yk) = ( i )i + ( i )j + ( i )k

A: We will find the curl.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = ti + t5j K(t):

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Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

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Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

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Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

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Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Sy³/y² + 9dy

A: ∫ y3y2+9dyLet u=y2+9=∫u2-9u2du=∫ u4-9u2du=∫ u4du-∫ 9u2du=u55-3u3Substitute back…

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

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Q: (D2 – 1)y = 2e-*(1+e-2*)-2, %3D

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Q: S 2y(yª – 4)¯³ dy

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