S tan-1 е' 1+4t² 2t dt

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A: Given

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A: Solution of the problem as follows

Q: 8. Evaluate 2 (9x² - 10x + 6)dx

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Q: 6. Use a change of variables to evaluate | 23e2x4+7 dr.

A: Solution is given below..

Q: et R be the region below bounded by the parabola y and y = 0. (0,4) (1,3) R (-2,0) (-1,0) x and the…

A: definite integral

Q: Q4) Find the largest eigen value for the matrix A= 54 with x (0)=(7/17 1)

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Q: 15-18. Find the extrema of f(x) = 3x - 4x³ on the interval [0, 2].

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Q: Assume that the given figure is the graph of f'. y in

A: Local Maximum:It is a point within an interval at which function has maximum Value. Local Minimum:It…

Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: Directions: Complete the table below based on the given example. Answers for columns 3 to 5 must be…

A: the given problem is solved below in detail.

Q: e (lnx) ³ X ₁ J1 e dx

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Q: yields y'= 38263752. This means that when x-6 the function y: A) Decreases at the rate of 4782969…

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Q: x

A: Given problem:-

Q: lo 3 Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar…

A: Let's change given Cartesian integral to polar integral and then evaluate.

Q: π/3 7. Sp² sin 0 de dp π/6 8. (2-y)dy dx 9. 5/¹¹² x cos y dz dx dy

A: Since you have posted multiple sub parts question in this question which are not interlinked so i…

Q: Evaluate lim f(x), f(x) = (3x² + 5x − 1, (7x² - 2x - 3, x ≤ 2 x > 2

A: Topic:-  limit and continuity

Q: Find the general solution of the following linear first-order ODE (1-x²)y' +2y-x=2

A: We need to solve D.E.

Q: Solve the differential equation y"" + y = 3x² + sin x - 2 cos x

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Q: Find the area of the region bounded by the graph y = sin x, y = 0, x = 0 and x =3π/2

A: Area of a region when strip taken parallel to y-axis is ∬dydx.

Q: Find the value of the following mplicit derivative tan y-sec x=5 find...y'

A: Given query is to find the derivative of the expression.

Q: Show that the particular solution of the differential equation d²y dx² -6y-12(x+ e*) +5% dx 5 is…

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Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 62² and…

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Q: {CLO-2} Evaluate lim f(x) where (4x-1 if x3 O does not exist O 11 O 12 O 13

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Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: 3s - 8 4s² +25 3 COS (²) - 2 sin (²) Option 1 O None of the Choices 3 25 sin Option 5 8 COS sin…

A: This is a problem related to inverse laplace transform. Based on the general formula and concept we…

Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

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Q: (CLO-3) Find the area of the largest rectangle that can be inscribed in the region enclosed by the…

A: Given:-y=x2-5y=-x2+5let x=t  and -t are paramatric points on the curveboth the curves are…

Q: S sec³ x+esin sec x - dx

A:

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

A: Given :T(x,y)=x2+xy+y2-9x+3

Q: e critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: dP The population of a town grows at a rate defined by the differential equation dt population in…

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Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

A: We have to find the volume of the solid of revolution generated when the area described is rotated…

Q: 1. x² - 2xy + y² − 6x + 2 = 0

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Q: (b) Find the chromatic polynomial of G G

A: The number of distinct ways to color the vertices of a graph with certain number of colors is…

Q: If A = 4x³ and (a) TRUE (b) FALSE dt dx 2, then dA dt = 150.

A: As we know the Power law; ddxxn=nxn-1 Given: A=4x3 and dtdx=2

Q: For numbers 4-5, consider a plane bounded by the curve x = -y² + y +2 and the y-axis. The…

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Q: Evaluate the following integrals: 4x 6. ₁² x 3x²y²dy dx

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: 5. Solve the equation = 170. 6. Solve the following logarithmic equations. (a) log, (+5) = log, 3…

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Q: . In each part, find polar coordinates satisfying the state conditions for the point whose…

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Q: 3. F= F(x) = x² + x + 1, a = 1 to b = 3

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Laplace transform of the following functions a) cos3t b) (e^(2t)-e^(-2t))^2

A: Let's solve laplace transform of given function.

Q: Laplace transform of the following functions a) cos2tcos5t b) cos3t c) (e^(2t)-e^(-2t))^2

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: Find the Inverse Laplace of a) (3s-8)/(4s2+25) b) 2/3s+9 c) 5s+4/s3

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Q: Find the Laplace Transform of the following functions

A: Laplace Transform of function cos3t

Q: 1–2 = For each of the following functions given by power series, find f'(x) and f f(x) dx. Do not…

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Q: 2 4 cot 4 x dx

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Q: Given y=√√3x-2 0.09 dy= A (a) (b) (c) where x changes from x=2 to x=2.03. If the differential…

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Q: Determine whether the following function is differentiable at x = 9 f(x)=√x²-16, x<9 √x, x ≥9 (a)…

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Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…