Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t (0

Q: x+x-6 lim X-2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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: 7. a) Find the indefinite integral. (Remember to use absolute values where appropriate) 1 dx 4x -

A:

Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

A:

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

A:

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

A:

Q: Prove that n2 +1 > 2? when n is a positive integer with 1<n<4.

A:

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

A: Solution:

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

A:

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

A:

Q: Find the area between the curve y=2 and the chord joining the points (0,1) and (2,4). O 0.5608 O…

A:

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

A:

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

A:

Q: Given the curve v = x3 – 3x find the stationary or turning point

A:

Q: Product A and Product B are two different items manufactured by the same firm. Product A is…

A:

Q: y 3 y = V x 1 (1, 1) X = 8 y = X 2 4 6 8

A:

Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: Investigate the convergence of the following series. H.' 2n+5n 2) ΣΗ-1 ILJ! 3n

A: Here, the given series is: ∑n=1∞2n+5n3n Let, an=2n+5n3n; n≥1

Q: sin° xcos xdx x cos'

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

Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Write the expression as a single Integral 1. f f(x)dx + f(x)dx =, 2. S f(x)dx – , f(x)dx = 3. f…

A: Use the property of the definite integral; 1). ∫abfxdx=-∫bafxdx 2). ∫acfxdx=∫abfxdx+∫bcfxdx   1).…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

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

A:

Q: 4z² + 5dz 금(122+5) xo 4a? + 5 Part 2 of 2 ewrite the integrand in terms of u so that the integral…

A:

Q: Let ABCDEF is a regular hexagon with centre O. Let ā = 0A, b= OB and so on. Explain why/prove %3D…

A: We know that in an regular hexagon the distance from center to any vertex is same, then the…

Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

A: given function : f(x)=log3x and g(x)=2from figure it is clear that intersection of both curve is…

Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

A:

Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

A:

Q: 3x?+4x-7 ii) lim x2+9 X00

A: Given query is to find the value of the limit.

Q: Find the volume of the solid obtained by rotating the region bounded by y = 2° , y = 0, and z = 5,…

A: We have to find the volume of the solid.

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A:

Q: 17-20 Express the limit as a definite integral on the given interval. 17. lim sin x, Ax, t, [0, 7]

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

A:

Q: ах 2xy 2.xy +3y x +2xy dy dx

A:

Q: (a²- x²}3½ dx

A: see below the answer and calculation

Q: 21 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 3 9.…

A:

Q: x-4 \x – 4 Evaluate the limit. 1 11 lim x - 4 x2 + 3x – 28 X-4 Give your answer in exact form. If…

A: Given problem:-

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

A:

Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

A: Here, to find the volume of the paraboloid z=x2+y2+2 over the rectangle R=(x,y)∈ℝ2|-1≤x≤2, 0≤y≤2

Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

A:

Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

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: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Help Homer design a cylindrical silo to hold the output from his pet pig Harry Plopper. The silo…

A:

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

A: Explained below

Q: In(v¤) dædy 6. 15. Calculate ry

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: