If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

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A: To calculate the tangent plane for the function  at the point .

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Q: prove by definition 3/n and 1/n^2 converges to 0.

A: We need to prove that two sequences (3/n) and (1/n^2) converge to 0.We need to find that N in the…

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A: To find the area of the shaded region.

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Q: Convert the point from cylindrical coordinates to rectangular coordinates. Зл (x, y, z)= 6, × )

A: Given  cylindrical coordinate is .We know in rectangular coordinates,

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Q: (a) f(x) = x¹ + 3x³ + 3x² + 1

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

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Q: Find the derivative of the function. u(x) = (x² + 1) 8x² - 1 u'(x) = Need Help? X Read It Watch It

A: Given that the expression we have to find the derivative of the given expression so u'(x)=?

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A: The ellipse is given as,

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Q: If sin(A) = 0.59 and cos(A) < 0, determine: Be certain to express all answers to at least four…

A: Sin(2A) = 2sin(A) cos(A) Cos(2A) = cos2(A) - sin2(A)Tan(2A) =

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

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Q: Which linear function is represented by the standard form equation below? 4x + 5y=40 A f(x) = -x+8 B…

A: the standard form of equation is 4x+5y=40

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Q: Given sin(a)= and 0 < a </2, find the exact value of sin(a/2). Note: You are not allowed to use…

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Q: (7.3) Find the inverse Laplace transform, L-¹ 1 2s + 14 s² + 2s + 10.

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Q: 3x1 3х1 2x1 - - 6x2 + X 3 + 13x4 6x2 + 3x3 + 21x4 4x2 + 5x3 + 26x4 15 21 23

A: In this question, we will solve the linear equations.

Q: Use graph below to calculate the following: (a) f(f(2)) = (b) g(g(2)) = (c) f(g(4)) = (d) g(f(4)) =…

A: A graph of the functions  and  are given.The aim is to find the composite function values  and .

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Q: Find the first partial derivatives of the functio f(x, y, z) = xyz + xy2 + y2² + zx fx =

A: Given,

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Q: Use the Laplace transform to solve the initial-value problem, y"+y= 3; y(0) = 1, y'(0) = 1

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A: The given series .The aim is to check the convergence of the series.

Q: A manufacture has been selling 1550 television sets a week at $390 each. A market survey indicates…

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