Find the arc length of the graph of r(t) = eV2t¡ + e-V2tj+ 2tk, 0

Q: Two particles travel along the space curves r(t)and u(t). (If an answer does not exist, enter DNE.…

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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: Question 6 Evaluate JJ xy dA, where R is the region in y = x2 R A) 13/7 B) 16/3 18 20 2.

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-2 and y=x about…

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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 and x…

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Q: Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

A: We need to evaluate integral.

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

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Q: Find r'(t) %3D r'(t) = %3D

A: Given;  r(t)=6 sqrt(t)i +t2 sqrt(t)j +ln(t2)k.

Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: Consider the following functions. f(x) = 4 sin x g(x) = 4 cos 2x Sketch the region bounded by the…

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

Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…

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

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Q: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

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Q: Consider the vectors: a = -11î + 10j +–12k, b = 2î + -8j + -12K, c = -7î +-10j + 10k a) Find: bxc =…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We need to evaluate the following line integral ∫C-ydx+xdy Where,  C: y2 = 6x  from 6, 6 to 0, 0

Q: Evaluate the definite integral. (9ti + 3+j + Vik) dt 9ti + 3tj tk dt

A: Topic = Integration

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: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

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

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Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

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

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Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

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Q: 1) lim x100+500 ex

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the approximate area under the curve of f (X) =cos ( from x =0 tox=T, Using 4 trapezoids. 3 2.6…

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Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

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Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

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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: Зху dx + 4xy dy %3D i 63

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 6 1 lim t→+o \ 8t2+9' 6t (?, ?)

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Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

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Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

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

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Q: What is the measure of the apothem of the hexagonal base? (c) What is the area of the hexagonal…

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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: Use double integration to find the volume of the solid. ... 3x + 2y + 4z = 12

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Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

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

A: Let's find.

Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

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: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

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

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