Q3: Solve the following first order differential equations Use any method: 1. e + 2x dx + e x dy = 0 2. + 2y = cos(x) dx 3. y cos(x)dx + 3sin(x)dy = 0

Q: 1. What is the slope of the tangent line to the curve 4x2 - 9y² = 1 at point (3,2) ? b. - 27 8 a. 3 ...

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A: To find the area.under the arch

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your a...

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Q: Consider the points A(3, –3, 3), B(4, –5,0), C(-3, -4,0), and D(6, 2, –6). | (a) Find the volume of ...

A: AB→ =B-A      =(4, -5, 0)-(3, -3, 3)AB→ =(1, -2, -3)AC→ =C-A      =(-3, -4, 0)-(3, -3, 3)AC→ =(-6, -...

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Q: olve the bessel equatio

A: answer of given question is in step 2

Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx a...

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Q: Suppose that f(x, y) 3, and D = {(x, y) | æ² + y² < 16}. Then the double integral of f(r, y) over D ...

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Q: If the Reference angle was e: What are the angle in the 4 quadrants.

A: I am attaching image so that you understand each and every step.

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Q: 6. |x²e-2*dx

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Q: 1 dx V1 –x²

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Q: C. 2よx dり CSCO ウこ0)ウこ6 V coso.vdvdo CSCO ウニズ vcosodrde CSCO tano=2 Cosede tano=1 Tん O= tan'(1) %3D 3...

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Q: 2. Evaluate the iterated integral. b. So R dx dy -2 2х 4 a. o xy dy dx

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Q: 3. y = 12 – 3x, y= 4 – x2

A: Given query is to find the area bounded by the curves.

Q: 4. dx J x Inx VInx2 -1 A C - sec-1 (In xx) + C sec-1 - In x sec-1 (In x) + C + C In x. sec-1 O A В E...

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Q: The line passes through the point (-1, 4, -5) and is parallel to v = 2i – j. %3D

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Q: Consider the function below. x2 f(x) : x2 - 25

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Q: We now use the substitution u = x° + 8x and du = (9x8 + 8) dx to convert the entire integral into on...

A: Given the integral  ∫9x8 + 8x9 + 8x2 dx We now use the substitution  u=x9+8x and du=9x8+8 dx.

Q: tan 2x lim 4.x4

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Q: r = sec(20)tan(28)

A: To find the derivative of the function.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) F(t) = 4t3 %3D L{f(t)} %3...

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Q: Determine y' by using the formula for the derivative of arcsine function. a. 1 b. sinx c. COSX d...

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Q: Estimate the slope of the tangent line at the point t = -7, for f(t) = 15t – 1. (Give your answer as...

A: Slope of tangent line

Q: 1. e (3xy-x)dx+e* dy = 0; when x = 0, y = -1 4 Ans. y =-- 1 3

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Q: Evaluate. S*+ 2y)dx dy 3.

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Q: S(1 – cos 0) csc²0 d0

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Q: Use differentials and the graph of f to approximate the following. (Round your answers to two decima...

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Q: Use the Laplace transform to solve the given initial-value problem. dy — у %3D 1, у(0) %3D 0 dt

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin(/2t), y(0) = 14,...

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Q: Determine whether each point lies on the line. x = -3 + t, y = 6t, z = 5 +t (a) (0, 18, 8) O Yes O N...

A: Line in 3D

Q: 3. ーメ y" = -6x (x²_2x +4) Cメナ)3(xー0 y = with (x +a>( x-1) O find

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Q: Y= cas Cex), Y= sinx, 0SXT

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Q: Sketch the region cnclosed by the given curves

A: y=x-2y=x-2

Q: h as suggested by the equ )dx +3(x+ 2y)dy = 0 whem

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Q: Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of...

A: One of the foci            =0,0    poleeccentricity                   = 4vertex nearest to pole = 2,...

Q: 3x + 3y = 3 42. 8. 4x + 2y %D ||

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Q: solve for 0 ≤ Θ < 2pi    ,                                            Θ = theta -cosΘ+sinΘ=1

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Q: 5. Find the area of the region contained inside the unit circle {x² +y? = 1} and outside the rose de...

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Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation! %...

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Q: Recall y" Second Derivafive Analy'sis goals O track intervals of positive $ = -6x(x²_ax+4) (xta)? (x...

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Q: Solve the shifted data IVP by the Laplace transform method showing your work in details. y"+3y'-4y=...

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Q: In this situation, finding the indefinite integral is most easily achieved using the method of integ...

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Q: 9. If 8000 dollars is invested in a bank account at an interest rate of 6 per cent per year, compoun...

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Q: Find the exact value of the cos 75° using a half-angle formula. cos 75° = 2+V3 :: 2-V3 :: 2-V3 VV3-2...

A: Let's find. 

Q: A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will us...

A: Answer: The solution is as given below: