Use double integration to find the area of the plane region enclosed by the given curves. y = 81 – x and y = 81 – 81x A = i

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e"i+ e*j к(t)

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A: Follow the procedure given below.

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Q: 5. lim X-0 e2x-1

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Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A: Given:    a)   Curve y=x3-x2-2x Curve cuts the x-axis at           x3-x2-2x=0           xx2-x-2=0…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz da dz dy = -36 J-24

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Q: Question 7 Use cylindrical shells to find the volume of the solid generated when the region enclosed…

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A: We are authorized to solve only one question, please repost remaining questions Differential…

Q: 6. lim (sinx)* X0+

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Q: Find div F and curl F if F (x, y, z) = 10e*V i – cos yj+ 3 sin zk. %3D div F= curl F=

A: div F=∂Fx∂x+∂Fy∂y+∂Fz∂z∂Fx∂x =ddx(10exy)=10y exy∂Fy∂y =ddy(-cos y)=sin y∂Fz∂z=ddz(3 sin2z)=3(2sinz…

Q: Solve the differential equation Integrating Factor by Inspection: ydx + x(x²y – 1)dy = 0

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Q: 1. Find the area enclosed by the given curve, the x-axis, and the given ordinates (a) The curve y =…

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Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

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A: Given query is to find the equation of the tangent at x = 1.

Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: f 1 1 3. The graphs of f(x) and g(x) are given above. Find the following: (i) S'(1), where S(x) =…

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Q: each of the following functions determine dr

A: Given query is to find the derivative of the expression.

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Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: 465.98 23.98 2.789 56.09 ATATA TTA TA

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Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

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Q: 3.) ž sin'(x)dx

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). ||r(t)||° r(t) = e#i+ etj K(t) =

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Q: Using appropriate substitution 9x2 – 4 dx X is equal to

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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