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

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

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: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

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: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

A:

Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: Evaluate I| xy dA where R is the region in y = x2 A) 13/7 B) 16/3 18 D) 20

A: We have to evaluate the integral.

Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 NOTE:…

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

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Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

A:

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

A: Given: y=2x-6x=0 and x=4

Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

A: Given problem:-

Q: .

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Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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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: Question 16 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x…

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Q: Find V· (V × F), if F(x, y, z) = 7e2*i+9xe³j – e=k. V · (V × F)

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Q: If 0 =. then sec(8) =1 (Write your answer in the simplest form, use fractions whenever applicable

A: Explanation of the answer is as follows

Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

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

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

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Jse a double integral to find the volume under the plane z = 38x + yand over the rectangle R = {(x,…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

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

A:

Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: A lunar module weighs 12 metric tons on the surface of the Earth. How much work is done in…

A: Given that: The weight of the lunar module on surface of the earth, We=12 metric-tons The height to…

Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

A:

Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

A:

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

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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 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: Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as…

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Q: Question 19 Evaluate JJ xy dA , where R is the region in ´(1, 3) (5, 3) R (2, 1) (4, 1) х А) 56 В)…

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Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

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

A:

Q: If e is an angle in standard position, Cot(@) > 0 and sec(e) <0, then the terminal side of 0 lies in…

A: Trigonometry

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: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

A:

Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

A:

Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.