For the formula at the given point, find the equation of the tangent line 5. y=x²e at the point (1,1/e)

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Q: - d the absolute maximum and minimum values of f(x) = x³ − 3x² − 9x + 10 on the interval 41.

A: we will find the required.

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Q: 23. What statement is not true? f(x) = #+3 if z>0 if a ≤ 0 a. limf(x) = 3 x →0* b. limf(x) = 0 _0个x

A: f(x)=x+3   if x>0-x     if x≤0

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A: Given :The surface area of this cylinder = 2πrr+hV=πr2h

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A: To Find : Inverse of the given matrix by using technology.…

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Q: Find f(x) if f"(?) = 12x^2+6x−4 and f(0) = 4 and f(2) = 10

A: f''(x)=12x2+6x-4f(0)=4f(2)=10∫xndx=xn+1n+1+c

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A: Given query is to find direction derivative.

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A: Here the functions are The area is given by

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Q: A price index was approximately 98.6 (base year 1992) at the beginning of 1991. If inflation…

A: Formula used A = P( 1 + R100 )t A = amount after time t P = initial amount R = rate

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Q: Find a plane containing the point (4,5,-7) and the line of intersection of the planes 7x + 7y8z = =…

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Q: Use the table to evaluate the following limits: 8 f(x) -27 8.9 -30.6 8.99 9 9.01 9.1 10 -30.96 13…

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Q: -5-4-3-2-1 + -2- -3 -4 lim f(x) = 2-16 lim f(x) = 2-1+ a Determine the following values. Enter "DNE"…

A: Note : according to our guidelines i can solve only first question please reroute the remaining one.…

Q: f"(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 4 f(0) = -sin (0) - cos(0) + (0) + 2 x

A: Given query is to find indicated function.

Q: Find the eigenvalues and a corresponding eigenvector to the matrix: -2 3 A=(7²8). 10

A: Form the characteristic elation and solve to get eigenvalues and the corresponding eigenvector.

Q: 5. (a) Find the parabola's vertex, focus, di i. (y + 2)2 = 8(x - 1)

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

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Q: Use the limit definition of partial derivatives to find fx(x, y) and f(x, y) f(x, y) = x² - 2xy + y²…

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A: The answer provided below has been developed in a clear step by step manner

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A: Given rectangular coordinates:- 0,63,6

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A: Suppose that a colony of beetles grows exponentially with doubling times 5 years. How many years…

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Q: (a) What is the equation of the plane passing through the points (2,0,0), (0,1,0), and (0,0,2)? (b)…

A: Given that plane passing trough the points (2,0,0),(0,1,0) and (0,0,2)

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Q: Find the points on the ellipse 3x² + y² = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: Find lim 1 2x217 a. x→ 0* 5 (x-6)2/7 b. x→ 0 as C. X→ 6* d. x→ 6

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Q: St²y" t²y" — 3ty' + 4y = t² ln t, [y(1)=1, _y′(1)= 1.

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Q: Use spherical coordinates to integrate f(x, y, z) = x² + y² + z² = 81. (Give an exact answer. Use…

A: Calculation of above requirement are as follows

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Q: find the revolution of the solid of revolution generated by revolving the region bounded by y=ln(x)…

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