Find the exact arc length of the curve on the given interval. Parametric Equations Interval x = 5 cos(8), y = 5 sin(0) 0 ≤OST

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: 3. Consider the piecewise function g(t) = ((t + 2)² +2 t≤0 t+6 t> 0° (a) Does g(t) have an absolute…

A: Let's find absolute maximum or minimum value of g(t).

Q: infinite

A: We have to find the value of the given definite integral according to the given information

Q: given that the graph of f(x) passes through the point (3,5) and that the slope of the tangent line…

A: The slope of the tangent line to the graph of y =f(x) at (a , b) is f '(a)

Q: Evaluate the definite integral. 2 da 4x + 5 [²³:

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

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Q: A river is flowing downstream at a constant rate of 5 ft/s. We take a rectangular net that is 6 ft…

A: Given river velocity ( v ) = 5 ftsrectangular net whose area is A A = length × breadth

Q: Use l'Hopital's Rule to evaluate commonly known limits. lim 0 x O lim Use l'Hopital's rule to…

A: Use  l hospital rule to find  the limit.

Q: You deposit $300 each month into an account earning 6.5% interest compounded monthl a) How much will…

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Q: Tutorial Exercise Find the area of the zone of a sphere formed by revolving the graph of y = √16 -…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  the derivative of…

Q: Calculate the Taylor polynomials T₂(x) and T²(x) centered at x = 2 for f(x) = ln(x + 1). T₂(x) =…

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Q: (D3 - 5D2 +8D-4)y = e2x, Find Y = Yc - Yp 1 =-=-=x² ₁²x 2_2x 2 a. C. C₁ et + C₂e O d. 2x b. C₁e² +…

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Q: Find the surface area of the part of the sphere x² + y² + z² = 100 that lies above the cone z = √x²…

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Q: Find the indefinite integral. (Use C for the constant of integration.) √x²ex/2 dx

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Q: Give a rational function that has the given graph. [You may leave the function in factored form.] 10…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A: The average daily metabolic rate for certain types of animals can be expressed as a function of mass…

Q: = converge or diverge? pply: Series Converges Diverges n=1

A: Topic:- sequence and series

Q: Find the center, foci, vertices, and eccentricity of the ellipse and sketch the graph. 16x² + y² =…

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Q: Find sin 2x, cos 2x, and tan 2x if cosx = sin 2x cos 2x tan 2x = 0) = 0 = 0 3 and x terminates in…

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Q: C. Verify by substitution that each given function is a solution of the given differential equation.…

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Q: Consider the vector field F = (x³y¹, x¹y³) Is this vector field Conservative? Select an answer If…

A: Solve the following

Q: (D2 - 3D + 2)y = ex, Find Yp -et O b. ex a. O-xex di xe O O e. none

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Q: 3 lim x→∞ x 4

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Q: Determine whether the series below is a geometric series, a p-series, an alternating series, or none…

A: According to question,Given Series,∑n=1∞ cos πn8n

Q: Evaluate the following limits: a) lim 1+ (1 + √/1² n b) lim x-0 1+x X c) lim(1+sin 4x) cotx x-0*

A: We have to solve Given limits.

Q: Find each limit, if it exists. If the limit does not exist, explain why. 1. lim x x² - x + 6 2 (x +…

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Q: (D3 - 2D2 - 5D +6)y=e4x, Find Yp

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

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

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

Q: Evaluate the definite integral [*2 sin(x)dx

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Q: Identify u and dv for finding the integral using integration by parts. (Do not evaluate the…

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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: Find the total work done if the motion is caused by the force field F(x, y, z) = (x+yz)i + (y+xz)j +…

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Q: Ify = Σo(k + 1)xk+3 then y' = Σο

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Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. da (463-1) 25 dt = ab…

A: Given query is to find the derivative.

Q: (a) (b) lim x→0+ lim -0←x (4---)) |x| (142/-/-)

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Q: Calculate the arc length of y = 3x + 1 as a varies from 0 to 1. S=

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Q: Consider the function f(x) Let F(x) be the antiderivative Then F(x) 6 x² of f(x) with F(1) = 0. ||||…

A: Solve the following

Q: maximum profit and the number of units that must be produced and sold in order to yield the maximum…

A: Given query is to find the production level for maximum profit.

Q: Draw the region whose area is given by the definite integral. 9 So (x+3) dx so 5 Which graph shows…

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Q: 10. dy_x²-3y² 2xy dx

A: 10. dydx = x2 - 3y22xyit is homogeneous equation with degree 2

Q: Compute (a) ₁ and (b) ₂ for the iterative process defined by n+1 = 2xn (4 — xn) with xo (a) x₁ = -…

A: Given query is to find x1 and x2 .

Q: Calculate Tu, Tu, and n(u, v) for the parametrized surface at the given point. Then find the…

A: NOTE: Refresh your page if you can't see any equations. . here we have u=5 and v=9 so the point…

Q: 7. dx dy 4y - 3x 2x-y

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Q: Find (as a unit vector with negative first term) an eigenvector of the matrix corresponding to the…

A: NOTE: Refresh your page if you can't see any equations. . and the given eigenvalue is

Q: They say the answer is 3; 2/3 i - j + 2/3 k. (where the first part is the length and the second part…

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

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Q: Establish the indefinite integral: f tanxdx A) In sinx|+C O B) −In\cosx| + C C) sec²x + C OD)-cotx +…

A: The given integral ∫tan x dx We have to evaluate this integral.

Q: 2) Graph 1 period of y = -3sin2x + 2

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Q: Evaluate the integral by interpreting it in terms of areas. 1₁ ( 4 + √9-x²) dx

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