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

Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

A:

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 5 sin(t)j…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

A:

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

A:

Q: dx 2.

A:

Q: (xy)=efr sin), Plo,0l Q(5,1)

A:

Q: (4x - lim (4x – V16x2 + 3x – 5

A: Topic:- limit calculation

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: A tank originally contains 100 gal of fresh water. Then water containing - Ib of salt per gallon is…

A: Given , A tank originally contains 100 gal of fresh water. Then water containing (1/2) lb of salt…

Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

A:

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

A:

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

A:

Q: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

Q: given point. Function Point f(x, y, z) = V x2 + y2 + z² (10, 3, 9) %3D Vf(10, 3, 9) = Find the…

A:

Q: Let f(x) = 9x* + nx² + e2x. Compute f((x). (Use symbolic notation and fractions where needed.) p)…

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: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

A:

Q: Use the Egyptian's formula to calculate the area of a circle with diameter of 8 units. (roundoff…

A:

Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A:

Q: Use a computer algebra system to approximate the iterated integral. (Round your answer to three…

A:

Q: E(-1)n+1_2 Vn n=1

A:

Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

A:

Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

A:

Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

A:

Q: Sketch the region R of integration and switch the order of integration. P(x, y) dy dx F(x, y) dy dx…

A: Given: I=∫-22∫x24fx,ydydx The region bounded by the curves y=x2, y=4 from x=-2 to x=2 is shown…

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

A:

Q: Evaluate the iterated integral: x + 4y dx dy Answer :

A: We can solve as follows

Q: ах 2xy 2.xy +3y x +2xy dy dx

A:

Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: A ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the…

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 iterated integral. /8 3/y sin y dz dx dy Jo

A:

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

A: Let's find.

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

A:

Q: (b) trte) × u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

A:

Q: X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

A:

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

A:

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 in Verse, then domain t range 8-X\ = (x)} OD:[8,8),R:[O,00) 2 All Real Numbers 8.00

A:

Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) 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: If the length of arc of a circle of radius 2/3 feet is 14 feet. then the central angle 0 is:

A: Given Radius of circle (r)=23feet & Length of arc (s)=14 feet To find central angle θ:

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B c) 0.5 D 3

A:

Q: A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the…

A: The given problem is solved below in detail.