t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

Q: dy ーy+x? -yx? ーソX

A: Given: dydx=1-y+x2-yx2

Q: ( sec(Inx) tan(lnx) dx

A: ∫seclnxtanlnxxdxLet u=lnx.=∫secutanudu=secu=seclnxAdd a constant to the solution=seclnx+C

Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

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Q: Please answer all parts in detail.

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Q: 8 Evelluate the double integral: + 3x) dydx

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A:

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A: Area of the circle , A =πr2, where 'r' is the radius of the circle.

Q: Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e-…

A: Integral

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A: Given that the point is on the terminal side of an angle in standard position. To find the exact…

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A:

Q: Consider the exact first order diff. equ: |M(x,y) = 2.xy- 3.x? N(x, y) = x² - 2y (I): (2xy - 3x )dx…

A:

Q: o} (2xy+y?) dx - 2x² dy = O 2.) xy dx -(x + 2y)? dn

A:

Q: Q2: Solve the following integrals:- (2) fd 4x2-9 xp: (3)fx sin(x +1)dx

A:

Q: Find the distance from A to C across the gorge illustrated in the figure. 130 ft The distance from A…

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Q: Find curl (8z i + 9x j+ 10y k). curl (8z i + 9x j+ 10y k) (i )i + ( i j + ( )k

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Q: 2. y = e*cos (2x) is a solution to y'-bytoy=0 3X

A: 2.y=e3xcos2x is a solution to y''-6y'+13y=0

Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

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Q: Vcsc² 0 – 1d0 [In (sin 0)]² + 23

A:

Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

A: Find your answer below

Q: Please

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Q: х- у 3. f(x, y, z) = y? + а. f(3, —1, 2) b. d. f(2, 2, 100) с.

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Q: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: answer

A:

Q: - sin² ydy 6. 4 tan" y

A: As per the guidelines I can solve only first question

Q: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

A:

Q: 4. x(x² – 1)² dx

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

Q: 18 of 20 Find the equation of the tangent line to the curve y = Vx+2 at the point (2, 2). y = 금z + 2…

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Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: Find the volume between the cone y = Vx² + z² and the sphere x2 + y² + z² = 25. volume =

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Q: xdx 46. S- V3+2x². – x+

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Q: Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall…

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Q: d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by…

A: Given that     r1(t) = cos(t)i + sin(t)j + 8tk    r2(t) = 7i + tk

Q: sketch the given region R and then find its area. R is the region bounded by lines y=x, y=-x, and…

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Q: 2. A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it…

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Q: anUNIVE Q3) Find the integration: - (x+1)vx2+2x

A: As you have asked multiple questions so I have answered only first question as per the…

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Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: у? — 4у — 21 Зу2 — 17у — 28 imy→7

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

Q: At a seaport, the depth of the water during the day can be found using the equation h = 6.0 cos (…

A: