2. 2. A = Fral eDen Value 2. 1- and eigen Vetor note

Q: 1 dx x (1+x4)4

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Q: Find y subject to the given conditions. y"= 12x, y"(0) = 14, y'(0) = 4, and y(0) = 4

A: To find y subject to given conditions.

Q: 4) Find the sum =1 an for the geometric sequence an = 10 - 3 %3D

A: The geometric sequence, an=10.3n-1

Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: compete Mž uing Values ा. ड 2 12 64 X010.5 511o5

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Q: onsider the functionfx) 5x" + 8x 1. f(x) has a critical point at x ind the value of A: A, does f(x)…

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Q: ||r(t) × r"(t)|| Use the formula K(t) to find «(t). r(t) = 5 cos(t)i + 5 sin(t)j + 4tk K(t):

A: Given rt=5costi+5sintj+4tkWe need to find kt by using the formula:kt=∥r't×r''t∥∥r't∥

Q: dx Let g(t) = | 4t

A: Given :g(t)=∫4tt4ex2dxFormula :ddx∫g(x)h(x)f(t)dt=f(h(x))h'(x)-f(g(x))g'(x)

Q: Write the sum using sigma notation: A 5+8+11+ 14+· + 44 > B, where ... TL 1 B 41

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Q: 12. Solve the second-Order differential equation: -y = e* (use method of variation of parameters)

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Q: 8) A rectangular storage container with a square base is to have a volume of 2250 inches cubed. The…

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Q: ||r(t) × r"(t)||. ||r(t)||* Use the formula k(t) : to find k(t). r(t) = t²i + t°j K(t)

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Q: 4. calculate JI, † (x, y, z) dS for the given surface and function. x² + y² + z² = 4, 0 < y < 1; f…

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Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The…

A: We need to find radius. NOTE - As per Bartleby's guidelines we can solve only one question from…

Q: Solve the following payoff matrix to find the best strategies and the value of game: B1 B2 Al 8 A2 3…

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Q: Evaluate the following integral. 3T s²x dx CoS Rewrite the second of the two integrals found above…

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Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: ind the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The figure inscribed in the sphere is needed to be maximized. So, volume of cylinder is to be…

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x3 + x)dx.

A: We need to estimate integral value. NOTE - As per Bartleby's guidelines we can solve only one…

Q: 2 4 - 8 Q - The determents|A| of matrix A =-1 - 3 6 is 7 - 2 c) -20 5 d) none of them a) -24 b)-32

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Q: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the…

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Q: can you explain the whole process, step-by-step? like in an essay type. how did they find the first…

A: Here the question is to find the first and second derivative of the function f(x) = 12cos2x. To find…

Q: 4.25 ft 11.8 ft 11.3 ft

A: answer is in next step

Q: Describe the graph of the equation. r= 18 cos ti - 9 sin tj - O tis an ellipse in thez = 1 plane,…

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Q: Match each function with its power series representation. Functions: Power Series: Function 1: 2 1…

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Q: Consider the function f(x) = 4x³ – 5æ on the interval [ – 4, 4]. Find the average or mean slope of…

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Q: 2. Convert (-V3,) to rectangular form.

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Q: 52.8706e-0.3277t h'(t) - (1 + 2.449e-0.327M;2 hes/year, where the child's height h(t) is measured in…

A: Given :

Q: Question 8 Evaluate the integral below by interpreting it in terms of areas. In other words, draw a…

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Q: 3) Verify that the hypotheses of Rolle's Theorem are satisfied on the given interval, and find all…

A: Solve the following

Q: 1 4 5 1 To find the blue shaded area above, we would calculate: 9. f(x)dx = area a Where: a = b =…

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Q: The line segment from (1, −1, 3) to (0, −3, 1) forms a diameter of the sphere S1. Find the…

A: We need to find equation of sphere.   NOTE - As per Bartleby's guidelines we can solve only one…

Q: Find the general solution of the following differential equation: (sin x)y' + (cos x)y = ex Then…

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Q: Q "- The value of e-(in+1)n is а) (-1)" e-я-1 b) (-1)"e" c) (-1)" e-*+1 d) (-1)" e- Q2 The period of…

A: e-ix = cosx -i sin x If y=A sinBx then period -2πB.

Q: Find f '(x). f0) = (+4)5 f(x) f '(x)=|

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Q: 3. Find the derivative of each of the following functions. Justify your answer. z sin z (a) f(x) =…

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Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

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Q: 5 5 5 The functions f and g are integrable and f(x)dx = 7, g(x)dx = 4, and f(x)dx =2. Evaluate the…

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Q: dx x3 4. Зх2 + dy y+1 -8(у + 1) %3D 0

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Q: 2. Solve the IVP: dy + 2y = te-2t, y(1) = 0 dt

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Q: Use the substitution u =x + 1 to evaluate the indefinite integral below. 5 1) dx Write the integrand…

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Q: Find solutions of the following equations by the method of separation of variables: 4. 2+= 0 at xe,…

A: 5.

Q: 1. Under what conditions will a set consisting of a single vector be linearly independent?

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Q: 3. Sketch the graphs of y = 4e -x, x = 4, x-axis and y-axis. Shade the region bounded by the curves.…

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Q: Find the nth term and the indicated term of the arithmetic sequence {a_(n)} whose initial term, a,…

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Q: (CLO-1) Three players (Ady, Brenden, and Cara) are sharing a pie that is worth $15. Suppose that the…

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Q: 7. Find the derivative of In y + exy? ey sin 2x. %3D -

A: Here, the given implicit function is: ln y+exy2-ey=sin 2x...(1)

Q: Determine whether n+1 converges or diverges. Give reasons for your answer.

A: Given: Here, an=n+1n2n. Notice that an=n+1n2n≈1n32. Now,                  limn→∞n+1n2n1n32=limn→∞…