Find the length of the curve: a) y=x^(3/2) +8 on the interval[0,2] b) x=(y^5)/5+1/(12y^3) on the interval[2,4](integrate with respect to y)

Q: ermine dy for the following two functions. dx y = 3x¹ + (7 + sin x)²

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Q: Create an inequality for the scenario below, identify the boundaries and points that are part of the…

A: Given: Shane and Abha are collecting cans and bottles. Each can earns = $1 Each bottles earns = $2…

Q: P 1/^ (1) J 8.

A: Given query is to find the integral.

Q: Evaluate the surface integral ffx dS, where S is part of the surface of a paraboloid with…

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Q: 6. Determine whether the series is convergent or divergent. If it converges, find the sum. Σ(++ (4)…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 5 sin(t). The initial…

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Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

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

Q: A 10 foot long ladder is leaning against a wall. If the top of the ladder is sliding down the wall…

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Q: Find the general antiderivative of f(x) = 3x5 + + C ت | يع +6√T

A: Given: f(x)=3x5+3x-4x2+6x

Q: Given the graph of the function f(x) below, use a right Riemann sum with 4 rectangles to approximate…

A: Graph of the function is given, we have to find the right Riemann sum using 4 rectangles to…

Q: Salmon swim up to 2000 miles upstream to spawn. Scientists have found that the oxygen consumption…

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Q: Which of the following is the antiderivative of f(x) = tan (A cos x + cotx + C B -In/cos.x+C (C) D…

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Q: 15 If ƒ [ f(x) dx = 1/2 and ["f(x) dx = 5, then [*f(x) dx =? A) 9/2 B) 5/2 (C) 19/2 (D) 25/2

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Q: For what values of p does the series below converge? Select the correct answer below: O p > 2 Op < 2…

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Q: Calculate: 4 x (-6) x (-8)                 (1 – 3 )(-2)(-4)   Given that m= -3, n = 2, p = -1…

A: To calculate the following  a). 4 x (-6) x (-8)  (1 – 3 )(-2)(-4)  Given that m= -3, n = 2, p = -1…

Q: 3. y" - 4y' + 3y = 2 cos x + 4 sin x

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Q: Suppose the derivative of a function f is f'(x) = (x + 1)4(x − 3)(x - 5)6. On what interval is f…

A: given function is    given that , derivative of a function is f'(x)=(x+1)4(x-3)7(x-5)6 for critical…

Q: Suppose that f' (3) = 0 and f" (3) < 0. Which of the following must occur at x = 3? (a) an…

A: we need to find out the correct option.

Q: Find the dimensions of the isosceles triangle of largest areathat can be inscribed in a circle of…

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Q: 4. y(2xy² − 3) dx + (3x²y² − 3x + 4y) dy = 0

A: Given differential equation y( 2xy2 - 3 )dx + ( 3x2y2 - 3x + 4y )dy = 0 standard form Mdx + Ndy = 0

Q: Consider the function f(x) = 8x¹0 + 10x52x¹ - 9. Enter the antiderivative of f(x) Question Help:…

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Q: Evaluate: ľ In(x) x² dx =

A: We have to solve given Questions.

Q: 2. (D4 + 5D²+4) y cos (3x +4

A: We need to find out the general solution of the differential equation.

Q: The height of a certain amusement park ride follows the function h(t) = +³+6t29t+ 4 where h is…

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Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0 0+

A: Given differential equation ( sinθ - 2rcos2θ )dr + rcosθ( 2rsinθ + 1 )dθ = 0 standard form Mdx + Ndy…

Q: 13. h(x) = f In 1 dt t

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Q: Evaluate the given integral: S 0 4 sin x cos x Cos 2x dx

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Q: What is the value of k in the equation (A) 5/3 B 3/5 5/8 25 on [ (3√/ x² +5√/\x³) dx = ²3x³¾/³ +…

A: The given integral ∫3x23+5x35dx=95x53+258xk+C We have to find the value of k.

Q: 4. rectangle has an area of 180 cm² and a perimeter of 54 cm. What are the dimensions of the…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

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Q: Question Determine the second derivative of the parametrically defined curve represented by the…

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Q: a. (2,2) 6 (131)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Problem 4. Find the local inima, local maxima, and for the functions: (a) f(x, y) = a¹ (b) g(x, y) =…

A: Please see the below picture for detailed solution.

Q: = 2+ sint, y = 1+3 cost. For what values of

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Q: 5 Σ(-1)", 4" n=1 20130 O Ο 5 04 0 -1 Ο 20 3

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Q: The following sum 36 - 6 (1) n 2 6 n + 36- 12 n 2 6 n + .. + 36- 6n n 2 6 n

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Q: Find the length of the polar curve r = 8 sin³ (0/3) on 0≤0 ≤π/4.

A: The arc length of a polar curve r=fθ between θ=a and θ=b is given by  ∫abr2+drdθ2dθ Given: r=8sin3θ3…

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

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Q: 4) Evaluate 0 2 X Je dy dx X

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Q: Let f: R → R be defined by f(x) = -5x - 7. Is f a linear transformation? -5xy-7 f(x) + f(y) = 5x-7 +…

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Q: Given the graph of the function f(x) below, use a left Riemann sum with 4 rectangles to approximate…

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Q: 2xD(D-3x)

A: Given: So,                2xDD-3x=2xD2-2xD(3x)=2xD2-2x(3)=2xD2-6x

Q: A particle is moving with acceleration a(t) = 24t+ 8. its position at time t = 0 is s(0) velocity at…

A: A particle is moving with acceleration a(t) = 24t + 8, its position at time t = 0 is s(0) = 16, and…

Q: Compute the flux of the vector field F(x, y, z) = 3i + 23 + 2k through the rectangular region with…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 2t, where 0 ≤ t ≤ 1.5…

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Q: Evaluate the surface integral ff 3x² ds, where S is part of the surface of a paraboloid with…

A: Given:- ∫∫S3x2ds S is part of surface of paraboloid with parameterization ru,v=vcosu,vsinu,v2 Where…

Q: Determine if the series converges or diverges. If the series converges, give its value.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the Taylor series generated by fat x = a. f(x) = 4x² + x² +4₁ a = -3 The Taylor series…

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Q: (x) = 7 sin(x) + 7 cos(x),    0 ≤ x ≤ 2? find concave up and down

A: Find the concave up and down of the function  f(x)= 7sinx + 7cosx , over the interval [0,2pi]

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

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