Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0. NOTE: Enter the exact answer. A

Q: 6. Find the length of the curve r(t) = t'i – 2/2tj + (t – 1)k for 0 st<1. |

A: To find the arc length of the curve rt=t2 i-22t j+t2-1 k for 0≤t≤1.

Q: 1+9n² b) Determine whether the sequence a, = converges or diverges. If it converges, %3D 1+n find…

A: The given sequence is: an=1+9n21+n2

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

A:

Q: Consider the limits. lim f(x) = 6 x-7 lim g(x) = -8 x→7 Evaluate the limit using the limit law for a…

A:

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

A:

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

A:

Q: Finden- un) andrn - in twe dferent mays r(t) -n+ se's - e'N, wt) - t'k (a) re) - uch) () Find the…

A:

Q: Find V x (V × F) if F(x, y, z) = 4.xyj+2xyz k. ▼ × (V × F) = %3D

A: ∇×F=i^j^k^∂∂x∂∂y∂∂zPQR  for a vector F=Pi+Qj+Rk in terms of x,y,z

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

A:

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A:

Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

Q: Find the area of the region using a double integral. The region bounded by y = 4x°, 2x + y = 6, and…

A:

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

A: Given; y=x^2 between x=1 to x=2

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

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

A:

Q: 1. E(n + -3 2 n=1

A:

Q: 2. Prove that the p-series converges for p > 1.

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A:

Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = T, using 4 trapezoids.…

A:

Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

A:

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: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

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

A:

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

A:

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: 2 2 3 Y= (4x3 - 4a3 ) 2

A:

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

A:

Q: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

A:

Q: moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3V2) (a) Find the…

A:

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: es ring (free) e 365 pursEval 2- -6 -5 -4 -3 -2 -1 Write an equation for the function graphed above.…

A:

Q: Find the area of the region using a double integral. The region bounded by y = 2x, x + y = 3, and…

A: To find the area of the region bounded by the given curves.

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

A:

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

A: Given

Q: 2" 5n+1 n=1

A:

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: 27. | (u + 2)(u - 3) du 2+x 29.

A:

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

Q: The position vector r describes the path cof an object moving in space. Position Vector Time r(t) -…

A:

Q: around the boundary of the parallelogram in the following figure (note the orientation (X9.Y), (2.0,…

A:

Q: Describe the graph of the equation. r = (5 – 31) i – 81 j O It is a line in 2-space that goes…

A: Given : r=(5-3t)i-8tj

Q: Find V × (V × F) if F(x, y, z) = 9xyj+2xyz k. V x (V × F)

A:

Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

A:

Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

A:

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

A:

Q: 2. Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

A: