Consider the following. 2 Find an equation of the ellipse. 12 62 Find its foci. –4 smaller x-value -2 (x, y): = y 8 4 2 1, -2 2 4 X 6 X

Q: 9) √ (72² - 4)=dx 2x (x²-4)* lx

A: I = ∫2xx2 - 44 dx

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Q: Find the sum of the series: 8 n=0 6n-3 n! xt

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Q: Find the surface area of the part of the plane z = 6 + 4x + 3y that lies inside the cylinder x² + y²…

A: To find the surface area of the part of the plane z = 6 + 4x + 3y that lies inside the cylinder x² +…

Q: Let u = (a, b, c) and v = (7, 8, 9). If u is parallel to (1, 0, -1) and the projection of u along v…

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Q: 56. Directrix: y = -3

A: To find the standard equation of the parabola with vertex at the origin  and having directrix y=-3.…

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A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

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Q: Compute the flux of the vector field (4, and (0,6) - xy2), out of the rectangle with vertices (0,0),…

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Q: luate ez²zds, where S is the part of the plane z = 3 + 2ª + y above the rectan 5] x [0, 4]

A: We have to evaluate the integral.

Q: x² +25 D)+ Xx Evaluate the following integral f (6) A) 4 Inx-21-In/x+31+ C C) 4 Inx-31-In/x+21+ C…

A: We use partial fractions to solve the given integral.

Q: Find the tangent plane to the surface z = cos(4xy) + x + 6y at the point (1,0). (z = cos(4xy) + x +…

A: z=cos4xy+x9+6y & the point is 1, 0. To find the equation of tangent plane.

Q: 6 Evaluate ay ds where C'is the right half of the circle x² + y² = 9 C Calculator Check Answer

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Q: COS √√2 2

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Q: 8) [x(x+2)³dx

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Q: Find the surface area of the part of the plane z = 6 + 2x + 3y that lies inside the cylinder x² + y²…

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Q: A triangle is defined by the three points: A = (10,4) B = (3,2) C = (8,5). Determine all three…

A: We have to find the angles in the triangle.

Q: The gradient of f(x, y) = e³² sin(3 - y) at (x, y) = (1, 2) is defined as followed: V f(x, y) =…

A: fx,y = e3x sin3y∇fx,y1,2 =( fx1,2 , fy1,2)

Q: A group of 100 people were surveyed about what hot drink they like and the results are in the table:…

A: Solution:A group of 100 people we surveyed about what hot drink they like and the results are in the…

Q: Find the average value of f(x)= cos x over the interval The average value is. (Tyne an exact answer…

A: The given function is f(x) = -cosx     We have to find the average value of f(x) over the interval…

Q: Find the volume of the region under the surface z = xy² and above the area bounded by x = y² and x +…

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Q: Find 1₁ (3x + 5y)dA where R is the parallelogram with vertices (0,0), (-3,3), (5,-4), and (2,-1). R…

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Q: Evaluate fry³da + zªdy, where C'is the rectangle with vertices (0,0), (2.0), (2,1), and (0,1)…

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Q: Textbook Given f"(z) Find ¹ƒ(²)= @Videos [+] = - -36 sin(6x) and f'(0) = -1 and f(0) = 4. Question…

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Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -180 feet per…

A: at=-32     v(t)=∫a(t) dtvt=-32t+C   when ball dropped , at t= 0 , v = 0 0=0+CC=0 Therefore  vt=-32t…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given that C'(x)=6x2-5xC(0)=5,000

Q: Find the flux of the vector field F = across the part of the plane z = 1+ 2x + 4y above the…

A: Vector field F=y,-z,xwe have to find  flux across the part of the plane z=1+2x+4y  above the…

Q: Sketch the region enclosed by the curves x - 6 = 2y and x - 10 = (y-2)², and compute its area. A =

A: Here we have to find the area of the region enclosed by the curve x=2y+6 and x=(y−2)2+10:-

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z)…

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Q: Find the tangent plane to the surface z = cos(6zy) +2³+7y at the point (1,0). (z = cos(6xy) + x³ +…

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Q: After 84 students at a particular university take a psychological evaluation, the sample mean score…

A: Given,   84 students at a particular university taken a psychological evaluation. The sample mean…

Q: Solve the system of equations using Cramer's Rule if it is applicable. 8x = 32 2x + 4y = 0 ww. Write…

A: We need to solve the given system using Cramer's Rule: 8x=322x+4y=0

Q: A differentiable function f(x, y) has the property that f(2, 2) = 5 and fx (2, 2) = -5 and fy(2, 2)…

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Q: Use the given graph of a function to answer the following. Assume the graph continues at both ends…

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Q: Suppose that f(x, y) = 2x + 1y at which -1 ≤ ≤ 1, -1 ≤ y ≤ 1. x

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Q: Find the equation of the tangent plane to the graph of f(x, y) = ln (4x² - y²) at the point (1, 1).…

A: The given curve is:f(x,y)=ln4x2-y2

Q: The gradient of f(x, y) = e³¹ sin(2 - y) at (x, y) = (2, -3) is defined as followed: - - V f(x, y) =…

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Q: 11. Mr. Gold wants to give her daughter $150,000 on the day of her 20th birthday by investing money…

A: To solve the following problem and find the solution

Q: Consider the vector field F = Evaluate ef F r(t) = t² i + t³j, 0≤ t ≤1 F. dr along the curve C:

A: Concept of line integral is as follows ∫F.dr→ = ∫t1t2F( r ).( dr )dtGiven F = < 7x + 5y , 5x + 2y…

Q: Question 5 Evaluate: a. 40 O b. 30 O c. 20 O d. 10 SS (3x²+9y²) dxdy 0 0

A: We have to evaluate the given double integral. Using power rule of integral- ∫xndx=xn+1n+1+c where c…

Q: (8) To evaluate f √√x²-49 x -.dx we substitute x = A)7 sec8 B) 7sine C) 7tane D) 7cose

A: We need to fin the substitution for 'x' to evaluate the integral: ∫x2-49xdx

Q: ,3x dx [x 10) [ xe 0

A: ∫01xe3x dx

Q: 7) [2x²e²* dx

A: Solving the problem

Q: 1₂0 xy¹ ds where C' is the right half of the circle x² + y² = 9 Evaluate

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Q: Suppose that f(x, y) = √√3² - ² - y² at which {(x, y) | x² + y² ≤ 3²}. +y=3 Then the double integral…

A: f(x,y)=32-x2-y2 at which {(x,y) | x2+y2≤32}

Q: Evaluate. (Assume x>0.) Check by differentiating. √(x+4) Inx dx

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Q: Find the divergence of the vector field F = div F = Calculator Check Answer

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Q: Use the substitution a = 75dx x²√√x²+4 22. 2 tan(0) to evaluate the indefinite integral

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Q: Find the general solution of the following differential equations USING ROO a. (D²+1)y = csCX b. d²y…

A: (a)   given (D2+1)=cosecx The auxiliary equation is m2+1=0 m=±i C.F = c1cosx+c2sinx…

Q: Find the points on the cone 2² = 2² + y2 that are closest to the point (1,2,0) Question Help Video

A: The cone is z2=x2+y2 that are closest to the point 1,2,0.