The function f(x) -2x³ + 30x² - 144x + 6 has one local minimum and one local maximum. This function has a local minimum at x = with value = and a local maximum at x = with value

Q: A farmer wants to build two adjacent rectangular pens sharing a common side. Each pen needs to be…

A: A farmer wants to build two adjacent rectangular pens sharing a common side. Each pen needs to be…

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Q: 1. The market research department of a company recommends that the company manufacture and market a…

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Q: Given the equation for a “tilted” ellipse: x^2-xy+y^2=3 . Find the points (x, y) on this ellipse…

A: Here we have to find the largest and smallest values of x.

Q: Set up an integral for finding the Laplace transform of the following function: f(t) = { 1 ²+5₂ t 5,…

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Q: Using the Inverse Function Theorem, what is (h−1)′(5) given that h(x)=−2x+14/−x−5? Note that…

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Q: a. Find the Laplace transform F(s) = L{f(t)} of the function f(t) = 2 + sin(6t), defined on the…

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Q: 1 [Ge Find nd 6e* dx

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Q: 12. fx²e-x dx 13. fx√x² - 4 dx 14. cos √t dt

A: The given integrals are;  13) x sqrt(x2-4) 14) cos[sqrt(t)].

Q: 10. Practice similar Help me with this Calculate the integral, if it converges. If it diverges,…

A: Here we have to find the definite integral.

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A: Topic = Application of derivative

Q: line to the graph of y = g(x) at x = 4 is 4x+12y = -56 It follows that y = is the equation of the…

A: Given that at x=4, 4x+12y=-56 is a tangent.

Q: For the function h(x,y) = 3x + y xy-6 əh find and ax dh ду

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Q: [6 sin [6 sin(8x) dx = [ Find 6 sin(8x) dx +C

A: To find the integral of 6sin(8x).

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Q: substitution method [ sin³ (7) cos (1) da dx 3

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Q: Find the interval of convergence of Σ M8 nt gan 24n

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Find all the second-order partial derivatives of the following function. h(x,y) = 9xey + 5y + 6 22n…

A: To find all the second-order partial derivatives of the following function. hx, y=9xey+5y+6

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A: Given integral:- ∫x2+5x2+1x-9x-8dx

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Q: By considering different paths of approach, show that the function below has no limit as (x,y) →…

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A: Comparison Test: Suppose we have two positive term series ∑n=0∞an  and ∑n=0∞bn such that an≤bn for…

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A: The answer is in step 2.

Q: Let L₁ be the line passing through the point P₁=(5, −1, −14) with direction vector №₁=[0, −1, −2]¹,…

A: Given:L1 : Line 1 passes through P15,-1,-14 and with direction vector d1→ = 0,-1,-2L2 : Line 2…

Q: (a) Compute s3 (the 3rd partial sum) of s = 83 7.25 71=1 Note: if giving a decimal approximation to…

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Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: What is the explicit solution of e^x(y^2+xy) = c ?

A: Given:exy2+xy=CAim: To find the explicit expression of the following formy = yx…

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Q: At what points is the function y = x+8 2 x-15x + 56 continuous? Describe the set of x-values where…

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Q: 5. Set up the integrals for the volumes of solids of revolution by revolving the triangu templates…

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Q: Find u and v if u+6v = 6i- k and 3u-v=i+j+ k. NOTE: Enter the exact answers in terms of i, j and k.…

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Q: 18. fcot'0 sin¹0 de 20. f cos³x sin 2x dx 22. ² sec (1/2) di

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

Q: Determine h′(x) if h(x)=(arccos(x))5.

A: Please see the below picture for detailed solution.

Q: Evaluate each integral. fæcos x cos(5x) dx

A: Integration by parts rule

Q: Evaluate the integral using partial fraction method S Evaluate the integral using integration by…

A: To find integral. As per our guidelines we are supposed to answer?️ only one question. Kindly repost…

Q: An object is moving with velocity (in ft/sec) v(t) = t² – 3t+4. At t = 0, the object has a position…

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Q: - Practice similar Help me with this Fill in the missing values in the table given if you know that…

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Q: Question 5 Find the volume of the body enclosed by a sphere x² + y² + z² = 4 and a cylinder x² + y²…

A: Find the volume?

Q: 2 1) Fird dy using implicit differentiation X² + y ²³ = 7xy 2) Find the ein of the normal line to…

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Q: Find the differential of the function. y = √5 + cos(0)

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Q: 1. S x(x) dx x(lnx)² sin 0 cos² 0-cos 0-2 2. S- 3. f x² tan-¹ (1) dx 4. f(cot ¹ x + tan¯¹ x) dx 5.…

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Q: Find y as a function of x if y" - 7y" +12y = 18e", y(0) = 25, y'(0) = 26, y'(0) = 25.

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Q: Evaluate the integral by making a u-substitution and then integrating by parts. ENOTE: Enter the…

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Q: If ƒ(x) = (6x² — 5) (4x + 2), find: ƒ'(x) = ƒ'(3) =

A: We have given function  fx=6x2-54x+2 f'x=ddxfx f'x=ddx(6x2-54x+2) f'x=6x2-5·ddx4x+2+4x+2·ddx6x2-5…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A: We have to find the vector in given question.

Q: $ Let F= (y.x) and C be the circle of radius 5 centered at the origin oriented counterclockwise.…

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Q: Evaluate the line integral Vp dr for the following function p and oriented curve C (a) using a…

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Q: Find the point on the curve y = √7x + 5 which is closest to the point (11,0). First find a function…

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