Evaluate the following Rational Fractions -(3 cos² 0 + 8 cose-12) sin 0 de cos³ 0+7cos² 0+ 12 cos 0 1. S (5x-12) dx 2. 3-6x²+8x 3. S dx (9-x) √x 4. f(x-1)(2x³+2x²+3x+2) dx x³ (x+1) 5. csc ³0 de S (9y+14) dy (y-2)(x²+4) ENGGMATH 4 FINALS PROBLEM SET 6. S.

Q: Find the general solution of the given higher-order differential equation. y"" - 8y" - 9y' = 0 y(x)…

A: The given differential equation is y'''-8y''-9y'=0 ............ (1)  Equation (1) can be rewritten…

Q: Solve the following inequality. (x+5)(x+3)(x-7) <0

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Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Use Newton's method with the specified initial approximation x₁ to find x3, the third approximation…

A: Given equation:- x5-x-5=0 , x1=1

Q: Use the functions below to find the given value. f(x) = x - 2 g(x) = x² | = (1)(₁_ 6+ z_ d)

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: Find all x-intercepts and y-intercepts of the graph of the function. f(x) = 2x³ + 12x² + 16x If…

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Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: Jse polar coordinates to describe the region shown. y -2 -1 1 1 2 Xx

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Q: Determine whether f(x) approaches or as x approaches 6 from the left and from the right. f(x) = sec…

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Q: Consider the following second-order differential equation. 3y" + 2y' + y = 0 Find all the roots of…

A: We have to find the general solution.

Q: Find Magnitude and Direction (Angle) Giving the Vector Given the vector u = -47 +17, find the…

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Q: (a) Area = ſ dx dy (b) Area = = [[ JJ dy dy dx

A: Follow the procedure given below.

Q: Use the equation Σ x" for [x] < n=0 (Express numbers in exact form. Use symbol 6 1 - x4 Σ 1 1-x Σ…

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Q: 19j isn't even an option... neither is your choices of + and - Please review possible answers and…

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Q: A rectangle is inscribed inside the curve y = √9 -x in the first quadrant so that the base is on the…

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Q: Use implicit differentiation to find dz/dx and dz/dy. X - z = arctan(yz) 218 дх 3: ду = = 1 22 yz +1…

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Q: Please solve part d)

A: To determine the points on the curve y=tan-1x, where the slope of the tangent line is the curve…

Q: Find the general solution of the differential equation y" - 2y + y = 7et 1+t2 NOTE: Use C₁ and C₂ as…

A: Given the differential equation is y''-2y'+y = 7et1+t2

Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞o). f₁(x)…

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Q: *T/2 10 cos(0) r dr de

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Q: Consider the following function. 1 f(x) = (x-4)² Determine whether f(x) approaches or - as x…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co).…

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Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: EX: Show that circle.it 10 Sol: Z= re io dzir e do 24 & dz = 2πi where c is a unit § C:1Z1 =1 10 ire…

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Q: When I put what you circled as an answer it tells me I am wrong so what part specifically is the…

A: You need not put the whole boxed expression as your answer.

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 n 4- 3 I 2 25 N -1 -2 -3 -4 74 ON 12 Select all…

A: Graph of the function is given, we have to find the limit and continuous at x=2

Q: Find the curve of best fit of the type y = aebx to the following data by the method of least…

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Q: part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the…

A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. - 1/2 (u = v), y = 1/2 (u…

A: Jacobian ∂(x,y)/∂(u,v)= ∂x/∂u* ∂y/∂v - ∂y/∂u* ∂x/∂v

Q: the Factor Theorem to determine whether x+2 is a factor of P(x) = 2x² + 3x² +4. cifically, evaluate…

A: Here given that x+2 is factor of p(x)  so according to factor theorem x+2 is the factor of p(x) then…

Q: 12. Let x be a positive real number and f(x) = log₁0x. Then f(10-x-2) is equal to: I1 f(x) B.…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: (d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the…

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Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, ∞o).…

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Q: ssume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: 6. Evaluate the following real integrals by residue theorem 3 • I- 88 151 +47 O dx (x²+1)(x² +9) ans…

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Q: Evaluate the integral. (Use C for the constant of integration.) s¯¹(x) dx COS

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Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: Solve the differential equation by variation of parameters. -t y" + 2y' + y = et In(t) y(t) =

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

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Q: Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a.…

A: This question is based on dot product.