Determine the modulus and the principle argument of the following complex number: (2 + 4i) (2 + 2i) 1 + i Z =

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A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: Bernoulli Differential Equation: Find the general solution 2 = x³y4 x dy dx y-³ = cx6 + 3²4 2y-3 =…

A: To solve differential equation

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A: Let's solve given diffrential equation.

Q: What is the area under the graph of y = 2 54-3-2-1 O O N/W 13 2 15 2 ਜਾਨ , -2+ -3 4 1 2 3 4 5 X on…

A: The region is bounded by the graph y=2-x on the interval -2,1

Q: Suppose that the nth term of the sequence of partial sums for a given series is Sn = 1+2n+3n² 4n²…

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Q: 5. Find the area of the region bounded by y=x² - 6x +5 and the x-axis. 125 (a) A= square units 3 (b)…

A: To find the area of the region bounded by given curves.

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Q: CHECKPOINT 1.24 Integrate the function [²₂x³dx.

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Q: Using the Limit Laws, find limt→0 (sqrt(t^(2)+9)-3)/(t^(2)). Do not use L'Hospital's Rule. plesase…

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Q: S Use The Fundamental Theorem of Calculus, Part 2 to evaluate X -4 dx.

A: A detailed solution is given below.

Q: Find the area bounded by r = cos 0 for -π/2 ≤ 0≤π/2. 2. Find the length of the r(t)= , 1 ≤t≤ 5 .…

A: We have to solve Questions 12.

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Q: 1 3x (2x + = + ₁). x+1 Find k'(x) if k(x) = 3x (2x + Provide your answer below: k'(x) =

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Q: (C) For what values of x does the series 11=1 (D) Find Taylor series at x=2 for the function ala…

A: series and taylor

Q: Solve the given differential equation by undetermined coefficients. y" + 2y' + y = sin(x) + 4…

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Q: 1. (a) Write the following set of equations in matrix form. 8=6X3+ 2X2 2-X₁=X3 5X₂+2X₁ = 13 (b)…

A: Here we have to write the equations in matrix form and then we have to do matrix multiplication.

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Q: Let P be the set of points that belong to the shaded region imaginary The set P is (A) open (B)…

A: We can see that the outer boundary is not included in the region. So set is not closed.  We can see…

Q: Find the general solution of the differential equation y" — y' - 12y -32t + 24t². NOTE: Use t as the…

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A: ∫vn dv =vn+1n+1+C .

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Q: 5. Iny+ea²²x+y = 10 -

A: Given :According to given , only 5 solvedlny+ex2y2-x+y=10

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A: fx=x2 over the interval 0,2 for n=4

Q: 12. Integral x² dx x³ +4

A: Given the integral,        ∫x2 dxx3+4

Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2. 2. Find the length of the r(t)= , 1 ≤ t ≤ 5…

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Q: A car drives down a road in such a way that its velocity (in m/sec) at time t (in sec) is v(t) =…

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Q: A region bounded by f(x) 8 7 6 Find the volume of the solid formed by revolving the region about the…

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Q: Find the solution of the initial value problem y" + 16y = 0, y (7) = 8, y¹ (17) ² Sketch the graph…

A: See this solution in below.

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Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

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Q: 13. Integral √x dx

A: Here we have to find the integral.

Q: Question 4. Determine if the series Σ n=1 5n+1 7-2 converges or diverges. If the series converges,…

A: We have to find the given series is convergent or divergent  , if the series is convergent give its…

Q: Let [ f(x) dx = 5, -6 Find and -3 [ f(x) dx = -4.5 -4.5 -3 6 (5 f(x) - 6) dx = f(x) dx = 6, f(x) dx…

A: The given integrals are;  f(x) , limit from -6 to -1.5. f(x), limit from -6 to -4.5. f(x), limit…

Q: (b) Using implicit differentiation Find the derivative of 1. y³ + 3x²y = 13 with respect to x and…

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Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

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A: Let's solve given integral.

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A: The symmetry means we can integrate from 0 to 1 and double the answer. x = 2 + y² opens right and…

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Q: Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t),…

A: To find parametric equations of the tangent line to the given curve.

Q: Solve the initial value problem y" - 2y' — 35y = 0, y(0) = a, y'(0) = −10. Find a so that the…

A: Here we have to solve the differential equation.

Q: The equations of the asymptotes of a hyperbola with transverse axis (focal axis) parallel to the…

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x-axis and the parabola x² +…

A: Graph:

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Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

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