2) Evaluate the integral S inx dr 2.

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A: Given; y^2+x^2=siny+4

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A:

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A: Find the derivatives by applying basic differentiation rules.

Q: 25. z arctan r dr dr 26. Jo (z – 1)² 27. e sin z dr

A: A detailed solution is given below.

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A: Volume

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A:

Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

Q: Find div F and curl F if F(x, y, z) = 17y®z*i – 8x'z®j – 4cy°k. %3D - div F= curl F=

A:

Q: Find the integral | 2(x* – x°)(x5 – 1)®dx а. b. In x2 dx 2х J x + 3)* С. 5.

A:

Q: Find the absolute maximum and minimum values of f(x, y) = (x^2)y of the set D = {(x, y): x ≥ 0, y ≥…

A: To find the maxima and minima first diffrenciate and then equate it to zero.

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Q: ind the volume of the shaded region when revolved about the indicated axis. 21 * = V7+y 14

A:

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Integral

Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

A:

Q: 7. S x4 sec (x5 - 9) dx 8. S tan 3 x dx

A: Question 7 and question 8 are solved.

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x2 – 9…

A: Given

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A:

Q: dx а. x V4+ln?x

A:

Q: Solve the differential equation Integrating Factor by Inspection: ydx + x(x²y – 1)dy = 0

A:

Q: 1. Maximizing. Determine the region R in the xy-plane that maximizes the value of SR S(9 – a2 –…

A: To determine the range .

Q: 3 Let F(t) = < 3 2t 3t -1' 3 - 5' 4 -3 Find F (t) F'(t) - < Question Help: D Video Add Work

A: Given: Now, we need to find r→'(t). r→'(t)=33t-1' , 2t3t2-5', 2t24t3-3'        =-93t-12,…

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A:

Q: -Find Taylor or Maclaurin for the following functions: 3) 2) f (x) = e* at a = 2

A: A detailed solution is given below.

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Q: Using Sandwich Theorem 3n? + 1 an = (-1)" n3 – 4 converges to 1 diverges converges to -1 none of…

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Q: (2a+1)(x–2) lim x00 (3x-1)(x+2

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

Q: Evaluate the triple integral. Xyz dV, where G is the solid in the first octant that is bounded by…

A: Integral

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Q: 2. lim (e* – 1)lnx X0+

A:

Q: 6. lim (sinx)*

A: u =eln u, then:limx→0+  (sin x)x  =limx→0+  ex ln(sinx)=limx→0+  eln(sinx)1x=elimx→0+  ln sin(x)1x

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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Q: Evaluate F• dr. F(x, у) — хі + уј = xi + yj C: r(t) = (7t + 9)i + tj, 0stsi

A:

Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

Q: if a 2. Then, lim f(x) =

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Q: -x lim + 169 x→-9 x+9

A:

Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: Definite Integral. 2.) S x²(2x³ + 1)*dx 4.) x?e*dx 6.) f- xp:

A: To integrate.

Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

Q: Evaluate the definite integral I (sin(t), cos(t))dt Add Work Submit Question

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Q: E(-1)" n n=1

A: Series

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Q: Question 7 Use cylindrical shells to find the volume of the solid generated when the region enclosed…

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Q: Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0.

A: Given   area can be given as below :

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2…

A: To write down that it satisfies the mean value theorem or not.

Q: Solve the general solution of Differential equation y''-5y'+4y=3e^{6x}

A: differential equation

Q: हम - (2) / हर्े 3

A: We can solve the given problem as follows:

Q: The integral TT tan x sec?x dx is an improper integral of type I that diverges is an improper…

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Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

A: