please answer the ff asap Consider the IVP: x" + x = 4et ; x(0) = 1, x'(0) = 3.

Q: A particle is moving on a straight line has acceleration a=5-3t and it's velocity at time=2. If s(t)…

A: Solution: a = 5-3t v(2)=7 s(2) - s(1)=?

Q: Find the area of the triangle with vertices P(1, 3, –3), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

A: Here, PQ=Q-P=0,0,0-1,3,-3=-1,-3,3PR=R-P=4,5,1-1,3,-3=3,2,4

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: 1. Given: - 4r? with f'(x) = (x+2)2 (r+8)(r - 2) (x+2)3 8(7r-4) (r+2)4 f(r) = and f"(x) = %3D %3D…

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Q: Find the demand function q = D(x), given the following elasticity conditions. E(x) = q = 205 when x=…

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Q: Find the location at t = 3 of a particle whose path satisfies dr 14t 4 dt (t + 1)² r(0) = (8,5) (Use…

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Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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Q: Let p(x) = x° + 10x- 36x3 + 36x² – 37x + 26. What is the relationship between p(x) and f(x) = 5x +…

A: The objective of the question is choose the correct option.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find an equation of the plane that is parallel to the plane x + 3y – 8z + 18 = 0 and contains the…

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Q: 2. Evaluate the following limits. x2-4x+4 a. lim x→5 x*-8x³+24x²–36x+16

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Q: 4. x - 3

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Q: Calculate the Taylor polynomials T and T3 centered at x = a for the function f(x) = 17 In (x + 1), a…

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 27 –14a5 –30z² +36x –8 2y5 -2x+2 dy %3D dæ 27+15* –…

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (10, 0) Vg(10, 0) =

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Q: alculate V3 + 2i. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 2n.

A: Given query is to find the value of a and b.

Q: Find the exact arc length of the curve over the stated interval. y = 7x2/3, from x = 1 to x = 8…

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Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

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Q: 12. Solve the following initial value problem: dy =3 dz VE-1 sin(y)' v(1) = 0. Make sure you write…

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Q: 1. State the domain and range of {(x, y)|y = + 3}.

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Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

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Q: A company determines that its marginal cost, in dollars, for producing x units of a product is given…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

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Q: Consider the Taylor polynomial T,(x) centered at x = 20 for all n for the function f(x) = , where i…

A: Solution: f(x)=1x-1

Q: 2. Evaluate the following limits. 4x2+x-7 f. lim 2x2+3x+10 X→-00

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

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Q: Determine whether the series converges or diverges. If it converges, find its sum. 3m m=2 Select the…

A: The given series is 7/3m .

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v…

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Q: af when r = 2, t =- 1 of the function ar 4. Use the Chain Rule to find- f(x, y, z) = e3xy² cos 2xyz…

A: This is a problem related to chain rule for differentiation. Based on the formula we will find out…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (3, –4)…

A: A detailed solution is given below

Q: A factory selling cell phones has a marginal cost function C'(x)=0.01x^2-3x+229 where x represents…

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Q: n: - 4.r? with f'(x) = (x+ 2)2 r(r+8)(r – 2) (x + 2)3 8(7.r – 4) - f(r) = and f"(x) = %3D %3D %3D…

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Q: Determine if the following statement is true or false. The points P,(2, 0, 1), P2(3, – 2, – 3),…

A: We know that three points P1, P2, P3 lie on the same line if direction ratios of P1P2 and P2P3 are…

Q: dv 9. S- V3v-2a 10. S(5 – 3y)*dy

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Q: f(x) = |x + 1| (-1,0) Prove that has no tangent line at

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Q: s+2 s(s-3) 25 s(s-2)

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Q: Determine the sum of the following series. 1" + 6" 8n п-1

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Q: а. у %3D х-5 — 4х* + 5х-3 -10х — 20 4x4 + 5x-3

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Q: Verify that y = cos x and y = sin x are solutions of the DE y” + y = 0. Are any of the following…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = ry + z²; P(-4,–3,4);…

A: We need to find directional derivative.

Q: To test this series for convergence 4" - 1 1 You could use the Limit Comparison Test, comparing it…

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Q: Solve the following and show the complete solution. 1. Find Duf at P: f(x, y) = sin(8x – 5y); P…

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Q: Find the derivative of the function described. (Rx5) 1. y = (2x + 3) (5x – 4)

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

Q: -4x2 f(r): r(r+8)(r – 2) (x+2)3 8(7r - 4) (x+2)4 with f'(r) = and f"(x): (r + 2)2 ' a. Find the…

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Q: 4. By using Taylor series, show that e* =cosx+i.sin x.

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Q: 6" We want to determine if the sequence is monotonic. (3п)! Using the ratio test we get that n+1 Sn…

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Q: he table shows speedometer readings at 10-second intervals during a 1-minute period for a car racing…

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Q: 2) A cuboid has a square base of side x cm. The height of the cuboid is ½ times the length of the…

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Q: Test the series below for convergence using the Ratio Test. n+5 52n +4 The limit of the ratio test…

A: Given