5. Using Green's theorem evaluate ſ [(x² + y²)dx − 14xy dy], where C is the closed curve of the region bounded by y² = x and x² = y.

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A: Inverse laplace

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A: Given that , y=6cosx and y=15x2-7

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A: To evaluate the following  integral by changing to cylindrical coordinates. ∫-33∫09-x2∫09-x2-y2x2+y2…

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Q: (a) (3√/3, 3) (i) Find polar coordinates (r, 0) of the point, where r> 0 and 0 ≤ 0 < 2πt. (r, 8) =…

A: According to our guidelines we are supposed to answer only the first question.

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Q: In Problems 1-10, solve the given differential equation by using an appropriate substitution. 8. dy…

A: To solve the following differential equation by using an appropriate substitution. dydx=x+3y3x+y…

Q: $1850 is invested at 5.5% compounded continuously. How long will it take for the balance to reach…

A: P=$1850A=$3700r=5.5%=5.5100=0.055

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A: Firstly we find local maxima or minima . secondly inflection point.

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Q: Estimate the area under the graph of f(x) = 21-a² n [0, 4] by dividing [0, 4] into four equal…

A: We need to find the area under the curve using the right endpoint rule.

Q: The integral 1 da can be rewritten as ff(u) du by making the substitution u = 5 x + 4. √5x+4 What is…

A: ∫15x+4dx

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Q: Find the most general antiderivative for the function Antiderivative = ? 6 -

A: ⇒fx=6x3-4x23

Q: 1. An arrow is shot into the air and its height in feet after t seconds is given by the function…

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Q: Use spherical coordinates. Evaluate (x² + y²) dv, where E lies between the spheres x² + y² + z² = 1…

A: We have to use spherical coordinates to evaluate the integral.

Q: Find the first few coefficients. Co C1 C₂ = C3 || C4 || || || The Taylor series for f(x) = e* at x =…

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Q: Find or evaluate the integral (Please show steps) J cos(x) 3+ sin(x) dx

A: to find out the integration.

Q: Change from rectangular to cylindrical coordinates. (Letr ≥ 0 and 0 ≤ 0 ≤ 2л.) (a) (-3, 3, 3) (b)…

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Q: (1) Find the absolute maximum and/or minimum points and values for r(x)=on (3,7).

A: rx=x2-5x-3 , x∈3,7

Q: Evaluating an Iterated Integral In Exercises 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,…

A:

Q: (7) Find the local linear approximation of f(x)=√2+3 at ro = - and use it to estimate the value of…

A: fx=12x+3

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Q: Use cylindrical coordinates. JJJ V √x² + y² dv, where E is the region that lies inside the cylinder…

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Q: 67. An early limit Working in the early 1600s, the mathematicians Wallis, Pascal, and Fermat wanted…

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Q: Let f(x)=x²-6x +2 Find coordinate of the minimum point, using derivative. O (-1,-7) (3,-7) (3,7)…

A: fx = x2-6x+2

Q: Assume that f is a one-to-one function. (a) If f(7) = 17, find f-¹(17). (b) If f¹(4)= 3, find f(3).

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A: The rate of change of a function f(x) with respect to x is f '(x)

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Q: Evaluate the indefinite integral. [x√3-x² dx

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Q: A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 2cos(t) for…

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Q: Given and ƒ¹(−1) = −5 and ƒ(−1) = 0. Find ƒ'(x) = 0 and find f(1) = = f"(2)=5x+1

A: given f''(x)=5x+1f'(-1)=-5  and f(-1)=0we know ∫xndx=xn+1n+1+c

Q: Use the Leading Coefficient test to determine the right and left end behavior of the following…

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Q: 2) f(x,y)=3(y² + x²y)³

A:

Q: Use the Root Test to determine whether the series is convergent or divergent. 00 Σ (² + 2)²² 1+ n n…

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Q: 3) f (x, y) = - 3ху x² + y

A: fx,y=3xyx2+y

Q: Please solve this

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Q: Solve the following DE: y" = 3[(y)² + 1]

A: Differential equation

Q: 4) Find the mass of a sphere of radius 4 if d = ko, k a constant. A) 16kл B) 256kπ C) 64k7 D) 512kT

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Q: Show that the value of f(x) approaches the value of g(x) as x increases without bound graphically…

A: f(x)=(1+3x)x and g(x)=e3

Q: Find the most general antiderivative for the function 8x² 4 6 x5 3

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Q: Sketch the graph using radians by creating a table of coordinates pairs using domains -2 π to 2 π,…

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Q: Identify the coordinates of any local and absolute extreme points and inflection Graph the function.…

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Q: The cost of fuel per hour for running a ship is proportional to the cube of the speed and is P1,350…

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Q: Evaluate the indefinite integral. Answer: +C cos(5x) dx 1+ sin² (5x)

A: