64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0, x=0 in the 1st quarter?

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: We have to find area bounded by the given curve.

Q: dy -(x²+y) B)Solve differential equation = dx x+siny

A: Here we have to solve the differential equation.

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: Find the average value f of the function f on the given interval. ave f(x) = 6x - x², [0, 2]

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: dy B)Solve differential equation dx -(x²+y) x+siny

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

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Q: B)Evaluate the integrals: i) f/2 inzerdrde " 0 ii) f/25/2 sinx 2² siny dz dy dx. π/2

A: B.1. According to question,Given Integral,Let I = ∫0π2∫0sin 2θr dr dθ

Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: The function f is continuous at a number c.

Q: Solve by Gaussian-Jordan algorithm (reducing to rref). Show all row operations you apply. If the…

A: First we reduce in row eclehon form .

Q: 2. Find the domain for the following functions: x 4 3x a) b) c) √√x-7 x²+x-56 x²+4

A: As per Bartleby guidelines rule I am answering only three sub-part of a question. This question is…

Q: Find the general indefinite integral. (Use C for the constant of integration.) [(7x² + 8 + 2²1) dx +

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Q: -)Find volume of body from above Z=√√4x² - y² and below Z Triple integration. 1 using

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Q: Solve the initial value problem y" + y = 0, y(3) = 8, y'(n/3) = − 16 Oy(t) = √√√3cost + 8√/3sint…

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.

Q: ) identify the technique of integration most appropriate b.) Find the average value

A: Here we have to use the concept of integration

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B. cos…

A: According to bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Find the rate of change of the area of a square with respect to the length z of a diagonal when z =…

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Q: Find and sketch the domain of the function. f(x, y) = √√√√4x²-√√25-y² O -6 DO -4 -6F 4 6 -6 -4 4 4…

A: The set of points (x, y) where the function f(x, y) is called the domain of f(x,y).

Q: A balloon rises at a rate of 3 meters per second from a point on the ground 60 meters from an…

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Q: Let f: A→B be a function, and X⊆A.Prove or disprove: f(f^−1(f(X)))=f(X).

A: Let f: A→B be a function, and X⊆A.Prove or disprove: f(f^−1(f(X)))=f(X)

Q: Fill in the blanks: x² + The equation describes an ellipse. The volume of the solid obtained by…

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Q: The total cost (in dollars) of producing x food processors is C(x) = 1600+50x-0.4x². Find the…

A: Derivative of total cost function gives the marginal cost function

Q: Determine the Cartesian equation of a plane that passes through a point (2,1,-5) and perpendicular…

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Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 + 6,    (3, 1)

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Q: Consider the following curve. y = (x+2)/(x-6) Find the slope m of the tangent line at the point (5,…

A: Here we have to use the concept of derivatives

Q: Find an equation of the tangent line to the graph of y = x³ 3x - 1 at the point (2, 1). - 09x+y+17 =…

A: We can solve this as follows:

Q: Bonus ( Show that given R: x € [0,1] Ay € [0,2] [[3x²yexydy dx = 6

A: See this solution in below

Q: Evaluate the following integral. 48x² S dx (x-15)(x+5)²

A: Solution of given question is written in below steps.

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Which expression below is equivalent to x4 − 4x³y + 6x²y² − 4xy³ + y4 O (x + y)4 (x - y)4 (x-2y)4

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Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

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Q: Find (-¹)(-5) using the Inverse Function Theorem, given that r(x) = −4x³ – 5x² – 7x – 11 . Note that…

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Q: In a Northwest Washington County, the speeding fines are determined by the formula: F(s) = 14(s -…

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Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: 11. What point on the curve y = x4, does the normal have a slope of 16

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Q: 1. The simplified form of the logarithmic expression log6 + 2log3 is a. log36 b. log54 c. log81 d.…

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Q: Solve the equation 2x-1= 3x+1 algebraically.

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Q: The voltage Vin a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: This question can be solved using the concept of rate of change.

Q: Consider the following equations. 3 y = 9- -1/2x², y = X₁ x = -2, x = 2 Sketch the region bounded by…

A: Here we have to find the area and the graph of the functions.

Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Find the interval of convergence of the power series: ∞ n [²(+1²] (x + 1)n 1)"] 2n n=0

A: To find the interval of convergence.

Q: Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: This question can be solved using the concept of angle between line and plane.

Q: B)Prove (cose + i sine)" = cosne + i sin no

A: Solution is given below:

Q: d dx (f³x²) = ○ 6x63x² (In b) ○ 6³x² (6 ln b) 6x6³x² ○ xb³x² (ln(6b))

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Q: S dx (36x² + 1)²

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Q: Evaluate x+1 S ex x² dx O e.e= + C O-e e + C O e e + C e = + C O

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