Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's list.) Theorem. (Enter your answers as a comma-separated f(x) = x + C = Need Help? X Read It

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A: Checking each option as shown below

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A: I am attaching image so that you understand each and every step.

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A: Use properties of functions

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A: We can find the length of the third piece.

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A: given f(x) = ( 4sinx + 6 cosx ) tan-1(x)f'(x) = ddx(4sinx + 6cosx )tan-1(x)f'(u.v) = udvdx + vdudx

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Q: 47. Find the area enclosed by the two curves below. v = x4 - 2 -X > I AM DONE

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A: The integral to be evaluated is  ∫x=-3x=0∫y=-x-1y=1-xe2y3-3y2-12y…

Q: 7 Graph R(x)= x² -+4x-5 x²+x-2 (lis steps, :) list all steps

A: Find the vertical asymptotes by setting the denominator equal to zero and solving for x. Since it is…

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A: Given query is to simplify the expression.

Q: H.W. solve the following equati.9.1.2.s. x + y = "1". ...........

A: Given differential equation:- y'=-2+e2x+y-1

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Q: 46. y = [x + (x + sin²x)³]4

A: Given y=x+x+sin2x34

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Q: Question Use a power series to represent the function f(x) Sorry, that's incorrect. Try again? £ £ 1…

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Q: Solve letter b. Intergal 5x/x^2-3x+2dx

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Q: 2 #fL = √ x² + y²₁ dL dt dx dt = 1, dy dt = -3, find (Simplify your answer.) dL dt when x = 12 and y…

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Q: Solve for the area of the portion of the surface S with equation z + 8x + 4y - 24 = 0 above the…

A: We can find the area of the portion of the surface S .

Q: Sand falls from a conveyor belt at a rate of 9 m³/min onto the top of a conical pile. The height of…

A: Topic - Application of derivatives We are given Rate of falling of sand from a conveyer belt = 9…

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A: The given sequence is; an=nsqrt(4n).

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Q: Estimate the value of Σ 3w|w n=1 n to within 0.024 of its exact value.

A: Given data, ∑n=1∞3n3

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Q: Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4.…

A: Graph of derivative function f'(x) for a function f(x) does not exist at x=c iff f(x) is not…

Q: Find the absolute min and max values of each function on the given interval. f(x) = x³ - 6x² - 15x +…

A: Given function f(x)=x3-6x2-15x+1

Q: 55-58 Find equations of the tangent line and normal line to the curve at the given point. √√x x + 1'…

A: We want to find equation of tangent line and normal line.

Q: Determine the singular points of the given differential equation. Classify each singular point as…

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Q: Find the limit of the rational function (a) as x→∞o and (b) as x→- 00. 2x 5 +7 x5-x²+x+2 f(x)= a.…

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Q: QUESTION 5 Given f(x,y) dA, where D is the region bounded by y = 2x² and y = 1 + x². Determine and…

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Q: 1 If f(x) = 2x sin−¹(x), find f'(x) = ƒ'(0.3) =

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Q: 5. Differentiate a) y²=3x²y+4xy² b) y=2x²-3x+1 2x+2

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Q: Verify Green's Theorem by evaluating both integrals [ 1² dx + x² dx = √ √ √ (²-8²) CA dy - /…

A: Given data÷ ∫cy2dx+x2dy Now we need to find the value of integral along C1,C2,C3,C4   1) For the…

Q: Given the function f(x) = x³ + 3x². 9x+5 over the interval −7 ≤ x ≤ 2, answer the following…

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Q: Power Series for Elementary Functions Function 1 = 1(x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)" (x -…

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Q: 25-32 Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Assume all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to…

A: Given query is to find charayof the graph.

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Q: An accelerometer has a damping ratio of 0.4 and a natural frequency of 18, 000 Hz. It is used to…

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Q: (a) What does it mean for f to be differentiable at a?(b) What is the relation between the…

A: (a) Let f(x) be a function which is differentiable at a point x=a.It means that the function is…

Q: For what value of a is the following function continuous at every x? a²x+2a, x≥2 12, X<2 f(x) =…

A: Topic = Functions

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Q: Use the definition of continuity and the properties of limits to show that the function is…

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Q: Find a Cartesian equation for the curve given by the polar equation T = 4 sin 0. 73°F 1. (x - 2)² +…

A: We have to find out

Q: 2.) Over the interval [1,6] f(x) 2. -2₁ HFF 4.4. H 0. QUE

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Q: Use the (a) y = quotient rule to differentiate e4x x² + 2 (b) y et In x

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

Q: 7.13. Use L'Hôpital's Rule to find the following limits: 24 - 81 26 - 64 z²+i (a). lim z→i z¹4 +1…

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