(3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

Q: 2. Evaluate all of the integrals. a. [² sec² x tan x (1 + secx)² dx

A:

Q: Does the Rolle's Theorem applies for f(z) – ln(2 – z²) over the interval [−1, 1]? O Cannot be…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: 1. Evaluate the assigned limit using L'Hopital's Rule. lim [cos (2x)]¹/(*-*) X-T

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Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A:

Q: Evaluate the integral: .0 ²/3 t ln u tan s ds du dt 2e π/3

A: Given: ∫-10∫e2e∫0π3t lnu tansdsdudt

Q: Find the equation of the logistic function with a maximum value of 1000, an initial value of 500,…

A: Topic:- function

Q: True or False? 4. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then…

A: according to the company rule we can answer only the first question and rust can be reposted.

Q: An integrating factor for the linear differential equation y' + = x is Select the correct answer. O…

A: This question can be solved using the concept of linear differential equation. Note: elna=a

Q: (x + 2)" Q4. Find the convergence interval and radius of the series : Σ (-1)**² n=l n

A: We need to find interval and radius of convergence.

Q: Evaluate: ³₁² [(x² - y²) ² x+y 21 du dt

A: The integration of the double integral is  (x2-y2)2/(x+y)

Q: Let R be the region enclosed by the polar curve r (0) = 1 + 2 cos² (0) where ㅠ 0≤0 ≤ iss 3

A: This is a problem related to area bounded by the region. Based on the formula of polar curve we will…

Q: 3. Determine if the assigned improper integral is convergent or divergent. Lever e²+1 dr

A: Given problem:-

Q: 3 Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

A: This is a problem related to triple integration. Based on the general formula and concept we will…

Q: ¹₁1+x²x+2y dy dx

A: We need to evaluate the following iterated integral as following: ∫-11∫2x21+x2x+2ydy dx

Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: 5x 2 Evaluate: f fx fdz dy dx 2

A:

Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: v (2uv²-3) du + (3u²v² − 3 + 4v)dv = 0 Ov(u²v² +3u + 2v) = c Ov(u²v² - 3u- 2v) = c Ov(u²v² - 3u+ 2v)…

A:

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

A:

Q: Q8. Solve the following D.E to find y as a function of x : dy dx y sin 2x 3y² cos2x

A:

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: Evaluate: ff xy² dx dy

A:

Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y 12…

A:

Q: To find the distance across a river, a surveyor chooses points A and B. which are x 450 ft apart on…

A: Consider

Q: If the total cost function is given by TC = 300+5g+then the marginal cost function MC = Ⓒa. 5g + / 3…

A: We have to solve the given 2 question.

Q: Find the area of the region bounded by the curves 1 (+6)² = 4 and the x-axis using vertical strip

A: using vertical strip we have  Area=∫-∞∞∫1x+624dydx

Q: Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the…

A:

Q: mydx = nxdy

A: answer is in next step . please give a like !!!

Q: PARKING THIS BLOCK 2AM TO 5AM 2 HOUR PARKING THIS BLOCK 9AM 6PM EXCEPT SUNDAYS 15 MINUTE PARKING…

A: Ques (a) According to the third sign (at the bottom), the parking time is between 8 AM to 5 PM. So…

Q: [s sec5 x tan4x dx

A:

Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

A:

Q: For the following graph of a function, estimate the area under the curve in the interval [-4, 2]…

A:

Q: For the following system: a) Determine how, if at all, the planes intersect. b) If they do,…

A: Given

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A:

Q: The value of A.cos(x²+)+C cos (x² + + C fx sin (x²+3) de dx B. - cos (x² + 5) + C D. -cos (x²+)+C

A: Option (B)

Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: Evaluate the integral: -2е π/3 ƒºƒ²² ƒ”¹/³ t ln u tans ds du dt see

A: Given

Q: 3 Evaluate: £³₂ √²₁ ₁²[z³(x + y)³] dz dy dx

A: Given :∫-23∫-12∫01z3x+y3dzdydx

Q: Find the area of the region bounded by the curves 1 y 5, y = 4 and the x-axis using vertical strip.…

A:

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

A:

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: Q4: Solve the follov A) Find and graph the volume generated by revolving the first quadrant area…

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Q: 2. Evaluate all of the integrals. b. 2|x - 21 dr

A:

Q: Be u = x2 + yz, where x = rsin(t), y = rcos(t) and z = rsin2(t), calculate: ∂u/∂r and ∂u/∂t

A: