H.W: Evaluate the integral 3 0 1 | (x?y – 2xy)dydx | |(x + y + 1)dxdy 1. 2. 0 -2 -1 -1 3 1 4 1 (2х — 4у)dydx | x*ydxdy 3. 4. 1 2 0 2π π 5. ||(sinx + cosy)dxdy

Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t< 7 L = e - e- - 0

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A: We have to find given expression.

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A: B is the correct option.

Q: 10 X=-3

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Q: Find each of the two areas bounded by the

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Q: tanx dx I+x?

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Q: Find curl (4zi+ 5xj+8yk). curl(4zi+ 5xj+ 8y k) = ( i )i + ( i )j+( i %3D

A: As we know that; The expression for the curl of the vector point function F→=F1i+F2j+F3k is; curl…

Q: I. Evaluate the following antiderivatives. tan (VT) + 2 1. TE (sec(/r) – cos(/#)) dx Cos(V))

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Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

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

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A: The given integral is Sin(3x)/[1+cos2(3x)].

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Q: Evaluate each integral. dr 1. VI² – 1 2. [zcos I Cos az dz 7x +1 dr 2-- 2 3. 7 – I – z

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Q: 6. Find y = f(x) given d²y = 5x? + 2 dx2 %3D

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A: To solve the differential equation by using method of undetermined coefficients.

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = eti+ etj K(t) :

A: Given r(t)=e5t i + e-t j

Q: Use sigma notation to write the Taylor series about x = xo for the function. e¬4x, xo 1 Taylor…

A: f(x)=e-4xf-14=ef'(x)=-4e-4xf'-14=-4ef''(x)=16e-4xf''(-14)=16ef'''(x)=-64e-4xf'''(-14)=-64e

Q: NOTE: Enter the exact answer. xe*y dy dx

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Q: 2.) f x²(2x³ + 1)5dx

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Q: 2) Use "TELESCOPE technique" to find x which is involved in INFINITE PROCESS. 4 4 4 4 4 4 4 X = 42…

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Q: am confused can you highlight answers please thank u

A: From the original solution the answers are: Intercept: 0, 0 Relative minimum: -5, -110 Relative…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5…

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A: This is a problem related to area calculation using integration. Please find the procedure given…

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Q: 5. Find the integral | 2(x* - x°) (x5 – 1)®dx x In(x + 2) dx а. d. | In x? dx | 2xe** dx b. е. 1 2x…

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: L. dr 16. (I + 2)² 1 dz 17. x(x+2) 18. / arctan Vr dr

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Q: (b) The curve y = x +3x, from x 1 to x = 3 (c) The ,2 1 from 2 to g

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

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Q: Evaluate the expression. 12 O A. 66 О в. 6 О с. 33 O D. 239,500,800

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Q: Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

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Q: Consider the integral cot(0) · In(6 sin(@)) d0: This can be transformed into a basic integral by…

A: We have to find the integral.

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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 .

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A: Given problem:-

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 V (V x F), if F(z, y, =) = 3e""i+7ze'j – 3e"k. V. (V x F) =

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Q: Use a triple integral to find the volume of the region bounded by z = 7x + 8y, z = 9, and the planes…

A: Let's find.

Q: y" — Зу + 9у — 0

A: Given; y''-3y'+9y=0

Q: The following telescoping series 00 1 Σ- en+1 – en+2 n=1 converges to Ve the above none of them…

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Q: 1. The sum of the digits of a two digit number is 15. One-third of the number diminished by 12 is…

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Q: 7. lim vx² + x + 1 – vx² + 1 X00

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Q: II. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) F'(x) lim = lim…

A: To evaluate the given limit of the function.

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A: This is a problem related to dot and cross product of vector. Based on the general formula and…

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.