Calculate the area of the segment cut from the curve y=x(3−x) by the line y=x. Also, sketch the graph.

Q: 3. Sketch the graphs of the curves y = 2x² + 1 and y=7-x. Shade the region bounded by the curves.…

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x². + +x+5)…

A: We have to find the one side limit

Q: Find the gradient of the function z(x, y) at the given point P: z = cos(x² + y²), P(3, — 4).

A: The given function is z=cos(x2+y2), P(3,-4).

Q: When I put what you circled as an answer it tells me I am wrong so what part specifically is the…

A: You need not put the whole boxed expression as your answer.

Q: -1 O -5 -10 -4 2, IP 2 IP 3 4 10 5 X X -1 y 10 -1⁰ IP 2 3 4 X -5 -4 -3 IP -2 -1

A: Topic:- application of derivatives

Q: Let v = (2, -1, 5) and u = (5, -7,3). Find 37 - 5u

A: We have to find 3v - 5u

Q: b) […. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x²…

A: Given :y=-x2+9y=x2+1

Q: Find the interest rate needed for an investment of $9,000 to triple in 7 years if interest is…

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Q: Given that logp q = x 2 and logq p = 1 2x−1 , find x

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Q: Find f   f '''(x) = cos(x),    f(0) = 7,    f '(0) = 6,    f ''(0) = 5

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Q: -1.0 -0.5 π/2 2 r = 1 + cos 0 0.5 1.0 1.5 2/0

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Q: Solve the equation for 8, where 0 ≤ 0 ≤ 2. (Enter your answers as a comma-separated list.) 2 cos²(e)…

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Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim +3) 6 +

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Q: (b) : Verify that the Intermediate Value Theorem applies to the indicated interval and find the…

A: Given , f(x)= x²-x in the interval [1,5]

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 2²-2y²-3²= -4…

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Q: QUESTION 2 a) Evaluate the area of a region that lies inside the circle x² + (y-3)2 = 9, but outside…

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Q: Evaluate the derivative of the following function. - f(x) = 18x sinh −1x − 180x2 + 1 f'(x) = 18 cosh…

A: To find the derivative f'(x)

Q: Example 13 Les A-[³3] and [3] A= B= Find AB and BA if they exist.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

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Q: LILL Hours spent studying 2 Graph B 4 6 8 Hours spent in class d. What is the equation for Graph B?…

A: Here s denotes study hours and c denotes hours spent in class.

Q: EX: Show that circle.it 10 Sol: Z= re io dzir e do 24 & dz = 2πi where c is a unit § C:1Z1 =1 10 ire…

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Q: etermine the Laplace Transfor f(t) = 3te-5t cos(2t) stands ca

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Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal places.…

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Q: Find Unit Vector Find a vector (u) with magnitude 6 in the opposite direction as 7 = (-5, 4) Give…

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Q: The Integral xy√√x² + y² dydx is equal to 1 Select one: O /(2√2+1) //(√2-1) 15 O /(2√2) /(2√2-1) O…

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Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: x-1 lim…

A: We need to find the limit limx→∞ x-12x2-7x

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

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Q: 1. Answer the questions below and then sketch the graph of the exponential function f(x) = (-)* + 1.…

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Q: find the derivative using implicit differentation

A: Apply derivative on both sides

Q: A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism…

A: Given :The spring is stretched 6 in by a mass that weighs 8 lband damping constant…

Q: The interest rate for a savings fund was 3.80% compounded semi-annualy for the first 4 years and…

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Q: Find the center, vertices, and foci of the ellipse 4x² + y²-8x+4y-8=0.

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Q: Divide. If the divisor contains 2 or more terms, use long division. 21x²-37x+12 7x-3 Divide. 5 9 4x…

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Q: How/why does f(x)=10/x become f(x)=10/x^2?

A: The process of how f(x)=1x become f'(x)=-10x2 has been explained in next step.

Q: Express the number as a ratio of integers. 1.325 1.325325325.... -

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Q: X (2-x) 6(E-x) Htx

A: The solution is given below

Q: (5). a. The length of one side of a square tile is 1½ feet. Determine the area of the tile in square…

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Q: Question 1 [ 1 a. [ Use the method of multipliers to find the extreme value(s) of f(x, y) = x² + y2…

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Q: Find the function f(x) such that f'(x)=e^(3x)-6x+2 and f(0)=1. Thank you.

A: We need find the function f(x) such that f'(x)=e3x-6x+2 and f(0)=1

Q: You want to buy a $243,000 home. You plan to pay 10% as a down payment, and take out a loan with a…

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Q: In y=e³ sinx

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Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

Q: 7. [2/3 Points] DETAILS fre PREVIOUS ANSWERS LARCALCET6 5.1.060. The minimum velocity required for…

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Q: Rewrite the equation in exponential form.   ln(b)=n

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Q: Megan leased a car for 5 years at a rate of 4.80% compounded monthly. It required her to make…

A: Total amount paid after 5 years or 60 months = 665 x 60 = $ 39900 Remaining amount that she can pay…

Q: (1) Use the definition to prove that if x₂ → 2 then (2x, +1)/x → 5/2.

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Q: (5) (a) For all n € N and a + 0, show that k=1 11 1 1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: The series is divergent. Select one: O True O False n Σ (-3)" n=3

A: