(1) Evaluate or determine the definite integral: •5п a) | sint|dt, b) ₁dt, c) fe-tdt.

Q: y"-y-2y = 0, y(0) = 0, y'(0) = 1.

A: The given differential equation is; y''-y'-2y=0, y(0)=0, y'(0)=1

Q: (D3-5D2+8D-4)y= 2x, Find Y = Yc - Yp 1 a. O b. c+ciải tế giớ OC 12²³x²= + 12²x²5+ [²³²] + x³²50 -2x…

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Q: Use the ratio test to determine if the series converges or diverges 2n n! Σ=1

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Q: Use the ratio test to dete mine if the series converges or diverges n (12²232) n! 100 2n=1

A: Explanation of the answer is as follows

Q: Find the general indefinite integral. (Use C for the constant of integration.) 8x³. -7√x 1. X dx

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Q: (D-5D + 8D-4)y = e, Find Y = Yc - Yp 1 Cate -21 2 a. Cetci 2t O b. 2x 2x C₁ et + C₂²1 +C₁₂re ² +…

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Q: Evaluate the surface integral. J[ ² S is the surface x = y + 3z², 0 ≤ y ≤ 1,0 ≤ z ≤ 5 z dS

A: Here we have to evaluate the given surface integral where S is the surface x=y+3z2 , 0<=y<=1,…

Q: If f(x) = [ sin(x) = ['(x) 6 3+ t² dt and g(y) = f(x) dx, find g (7). 6

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Q: Evaluate the definite integral    D=∫1/20sin(πt)dt. NOTE: Use exact values only. Do not provide a…

A: Given query is to find the integral.

Q: produced to achieve a maximum profit Manufacturing time per ski Finishing time per ski Downhill…

A: To solve the following problem

Q: Find the parametric equations for the line described below. 1. The line through the point P(4, -4,…

A: We have to find parametric equations for the line.

Q: If f(x) = x² + 6, g(x) = x - 8 and h(x)=√x, then f(g(h(x))) =

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Q: x² +1 (c) (Still: the function f is given by f(x) 1+z2.) What is the smallest area of a x² rectangle…

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Q: Evaluate the indefinite integral. x + 3 1² + 6x + 10 dz

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Q: Find the roots of (D4 + D² + 1) +1+√³ 1 ± √√√3 1± √3 2 2 -1 ± √3 2 - 0 1 + −1+ - 1 ± i√√3 2 e. none…

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Q: Consider the function f(x)=∫x04t5+4t4−t3+2t2−3t−5dt. Compute f′′(x)

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Q: Our goal is to estimate the rate of change of d(t) at precisely the time t = 3 se This will be…

A: Given: dt=61.490-t

Q: A yeast culture is growing at a rate of W' (t) = 0.3e0.11 grams per hour. Find the area between the…

A: A yeast culture is growing at a rate of W't=0.3e0.11t grams per hour. To find the area between the…

Q: Evaluate the indefinite integral. 5 sin³ (2) cos(x)dx = +C

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Q: (D2 - 3D + 2)y = ex, Find Yp O a.-ex O b.ex Oc-xex C. O d.xex O e. none

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Q: 1 7x6 (6-x) dx 0

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Q: Find the roots of (D4 + 4)y = 0 O a. +2i, ± 2i + 2 O b. 2+2i, ±i OC. 1 ±i, -1±i O d.-1 ± 1, 2+2i O…

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Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. a =…

A: The given sequence is: an=7-14n To determine whether the sequence with the given nth term is…

Q: 7x² + 4x-6 x² + 3x² . dx.

A: We first evalute partial fraction decomposition for the given function and then evaluate the value…

Q: Starting at age 35, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

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Q: For y=f(x)=9x3​, x=4​, and Δx=0.08 find   ​a) Δy for the given x and Δx ​values, ​b) dy=f ′(x)dx​,…

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Q: f(x) = sin лx π.χ

A: given function is  f(x) = sinπx⇒f(0)=sin(0)=0and…

Q: Let f(x) = √9-x² and g(x) = x + 1. Find the following functions and their corresponding domains: f+g…

A: Given f( x ) = 9-x2g( x ) = x + 1 as we know that domain = range of x values

Q: 9. Passes through the points (1, 2, 3), (3,-1, 4) and (1, 0, 1). ✔ 23

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Q: Find the rectangular coordinates (x, y, z) of the point with the cylindrical coordinates (6,2,2).…

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Q: 22 of 86 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 1. If y=xsinx, then dy dx (A) sin x + cos.x (B) sin x +…

A: Since, you have posted multiple questions, as per guidelines we are supposed to answer only first…

Q: You want to buy a new car. You can afford payments of $300 per month and can borrow the money at an…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-6x, n = 3

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Q: Given that "f(z)dx=14, what is "f(u)d da 3

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Q: (D3 - 4D²)y = 5, Find Yp 5x2 4 a. b. 5x² 4 C. 5x² 12 d. 5x² 12 e. none

A: Given that         (D3 - 4D2)y = 5

Q: Evaluate fry³dx + x³dy, where C' is the rectangle with vertices (0,0), (6,0), (6,2), and (0,2).

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Q: (a) sin (2x), c = 0.

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Q: The shape below contains a rectangle and four semi-circles. Round your responses to two decimal…

A: Let's find area and perimeter of given shape.

Q: Determine which of the following tests would be best to use to determine the convergence of the…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) J sin (2x) 6 + cos²(x) dx

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Q: ΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑ 2 3 4 5 6 7 8 9 με Graph of f 2 O -2- - 15. The graph of a…

A: Solution:f is continuous and h(x) = ∫0xf(t) dt and graph of f is given aboveFrom the graph,h(6) =…

Q: nterval of convergence for the power series Econvergence = n=2 n(x - 2)" 22n (Enter your answer as…

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Q: (D3-2D2-5D +6)y=e4x, Find Yp O a. 1 24 O b. 1 4x e O d. 9 O c. 1 6 4x e ∙e 4x 1 18 O e. none e 4x

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: A 300-gallon (gal) tank initially contains 75 lb of sugar dissolved in 100 gal of water. Brine…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: solution for the following differential equation (do not solve): y" +4y' + 4y = (3+x)e-2x

A: Topic:- solution of differential equation

Q: The speed of a particle in a test laboratory was noted every second for 3 seconds. The results are…

A: t0123v96.565.5a) as we know that distance using left end points = v(0) + v( 1 ) + v( 2 )3 - 0…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. ·S*· g'(x)…

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Q: 2. Let f(x)=√x. Find an equation of the tangent line to the graph of f at the point where x = 16 and…

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Q: If f(x) f'(x) = = x2 - 3 - t² dt then

A: ∫xndx=xn+1n+1+cdxndx=nxn-1dconstantdx=0