Kindly answer the question and provide a clear and correct solution. If I still get wrong explanations, I will leave negative remarks. Also, include the graph of the region described by the bounds.

Q: Consider the function f(x) = 3x² − 2x +9, 0≤ x ≤ 7. The absolute maximum of f(x) (on the given…

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Q: Find the eigenvalues of A³ for Enter the eigenvalues in increasing order. Eigenvalues of A³ are: i i…

A: Cayley Hamilton theorem and basic property of eigenvalues are used

Q: Find the critical numbers of the function 2x5 – 5x¹ – 10x³ – 4 and classify them using a = f(x)…

A: We need to find critical numbers and classify them.

Q: Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

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Q: calculate the area of that part of the surface z = 2xy which is bounded by the planes   x+y=1, x=0,…

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Q: Find the maximum and minimum values of the function ㅠ g(0) 60 7 sin(0) on the interval 0, = Minimum…

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Q: Which statement is TRUE about trigonometric functions? O a. The derivative of sin x, cos x and tan x…

A: The answer with explanation is given below:

Q: A farmer finds that if she plants 60 trees per acre, each tree will yield 40 bushels of fruit. She…

A: We need to find no. of trees.

Q: A normal line is a line that is perpendicular to the tangent line which touches a curve at one point…

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Q: Decompose v into two vectors v₁ and v₂, where v₁ is parallel to w and v₂ is orthogonal to w. v=2i+j…

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Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: For items 22-23: The equation of a curve is y = 5tanx. 22. What is the slope of the tangent line…

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Q: Solve simultaneously x (t) + x' (t) − y (t) + z' (t) = 4 y' (t) + z(t) = 0 2x(t)+y(t)+z(t)=0 where x…

A: Given the system of differential equations x(t)+x'(t)-y(t)+z'(t) = 4  ......(1) y'(t)+z(t) = 0…

Q: The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of…

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Q: [x²√√x + 17 dx

A: ∫ x2x+17dxLet u=x+17.=∫u-172udu=∫ u52-34u32+289udu=∫ u52du-∫ 34u32du+∫…

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: The given equation of the curve y=x2+6x+2

Q: A payment of $2,170 was due three years ago, and a payment of $1,850 is due today. What single…

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Q: (y-2)dx-(x-y-1)dy = 0

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Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

Q: If f(x) = 5x(sin x + cos x), what is f'(x)?

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Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…

Q: What is f' (5) given the function f (x) = O 0.48 O 0.048 O No correct answer O 0.049 0.49 /x-3 √T+3…

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Q: 1. Given the region bounded by the following functions as well as the x-axis: y= 2²/1₂ ² x= x = 4…

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Q: A scheduled payment of $4,000 due in one year is to be replaced with two payments: the first due in…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: SOLUTION-

Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², z(t) = lnt, t€ (-∞0, +∞0).…

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Q: How many inflection points does this function have? 2 0 1 2 ∞

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Q: Use a graphing utility to sketch the intersecting graphs of the equations and determine whether or…

A: topic- equations and their slopes

Q: The letters r and 0 represent polar coordinates. Write the given equation using rectangular coordin…

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Q: 4. f(x)=

A: The given function is: fx=5x2x+3   As we know that; The Power Law: ddxxn=nxn-1 The Quotient rule:…

Q: Find the slope of the tangent line to the curve below at the point (5, 3). √x + 4y + /5xy…

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Q: f (x) = - 4x² - 6x x²+3

A: Given f(x)=4x2-6xx2+3To find the derivatives:

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

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Q: derivative of y = e(sin⁡x) − sin⁡(ex)8

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: 9: (71

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Q: Find the maximum and minimum values of the function ㅠ g(0) 60 7 sin(0) on the interval 0, = Minimum…

A: Use first derivative to sketch curve of function g(theta)

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: (2x + 3y - 1) dx - 4 ( x + 1) dy = 0

A: Explained below

Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, t€ (-∞0, +∞0).…

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A: We have to find the population.

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: A fish is reeled in at a rate of 4.0 feet per second from a point 10 feet above the water (see…

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Q: 9. J et dx 10. 4лr² dr

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Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

A: To find equation of tangent line and then arc length of thegivencurve.

Q: Determine the absolute extrema of the function f(x) = (x-3)ex on the interval -1≤ x ≤ 3.

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Q: A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 114 ft/sec Not…

A: Given problem:- A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.…

Q: of the function f on the given interval. ave f(x) = 3x² + 8x, [-1, 5] Read It Master It Find the…

A: Let's find average value of given function.