Determine the volume of the solid obtained by rotating the region bounded by y=x^2-2 and y=x about the line y=4

Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2 A) 1/3 B) 1/4 © 1/5 D 1/6

A: To find the area enclosed between the two given curves.

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

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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

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Q: Given the following functions: f(x) = cos(x) g(x) = x + 1 Find f(g(x)) and 8(S(x). (Use symbolic…

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Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

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Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.

A: Explained below

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: 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: 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: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

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

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

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Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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

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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: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

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Q: L (21 +x+3)dx

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Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: x – 1 - V3x +1 lim Зх + 1 x→5 X – 5

A: Solution:

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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Q: Use the first six non-zero terms of the Maclaurin series expansions for sin x and cos x to…

A: From the Maclaurin series expansion of sin x and cos x: sin x≈x-x33!+x55!-x77!+x99!-x1111!cos…

Q: Use double integration to find the volume of the solid bounded by the paraboloid 2 = 9X- + y, below…

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

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Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 3 r(t) = e"i+ etj 9ts K(t) ||

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ei + Sin(/2)j + e stk…

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Q: Find the center of mass of the given system of point masses lying on the x-axis. - 6, - 3, m,- 6 X1…

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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: f" (x) = cos x, f(0) = 1, f'(0) = 2, f'"(0) = 3.

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Q: Use double integration to find the volume of the solid bounded by the paraboloid Z = 9x + y, below…

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: x'y'y'+ xy' = 1 dy x' + y' dx 2ху dy 2 rv + 3v2

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Q: sin° xcos xdx x cos'

A: We will use substitution method to solve this definite integral.

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

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Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

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

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Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

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

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

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Q: Find div F and curl F if F(x, y, z) = x°i – 2j + yzk. div F= curl F=

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Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

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