Given f and g are continuous functions and f(x) dx = -3 and g(x) dx = 5. What is [3f(x) + 2g(x)] dx ? O O 15

Q: Find the area bounded by x2 = 4y + 4 and x = y 2. Using vertical element, what is the integral…

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Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element. A…

A: Using vertical element form a double integral then solve it

Q: A closed wood storage having a volume of 27 in.3 is to be in the form of a right-circular cylinder.…

A: Volume of cylinder is πr^2h

Q: Consider the vector-valued function R(t) with Ả'(t) = (sec²(t − 1), - 2 Vt (a) Find R(t) given R(1)…

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Q: If x = t² and y = t³, then y O t 3/4t O 3/t Other: = ?

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: We need to find equation.

Q: (a-x)² (a-y)² (a-z)² Express (b-x)² (b-y)² (b-z)² as a product of two determinants and hence…

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: The tangent line to the curve at the point (1,2) also passes through the d² y point (-1,4). If at…

A: solution:-tangent passing through the point 1, 2 on the given curvealso passes through the point -1,…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Arearegion = [₁ f(x) dx + f[ g(x) dx,…

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Q: If web₁x-b₂y-b3z, w= where b₁,b2, b3 are constants and b² + b² + b = 1. Show that 8² w 8² w 8² w əx²…

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Q: (4) Find Laplace Transform F(s) for the variable x or y in the equations a- y" +2y'-3y=32e";…

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Q: terval of convergence of the series Σ(√n+1-√n)(x+2)" is given by -3<x<-1.

A: It is convergent when  |x+2|&lt;1  -1&lt;x+2&lt;1  -3&lt;x&lt;-1

Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: Evaluate the following double integral over the given region R. [[ 2 ln(x + 1) (x + 1)y Use…

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Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

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Q: (4) Find Laplace Transform F(s) for the variable x or y in the equations a-y"+2y'-3y=32e"; y'(0) =…

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Q: 2. Using your calculator, determine how many solutions the system has. Then without a calculator,…

A: This question is based on solution of Polar function.

Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

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Q: The interval of convergence of the series Σ(√n+1-√√n) (x+2)" is given by A=0 A-3≤x<-1. OB-3<x≤-1.…

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Q: The value of a is Blank 1. [²1² sin³r cos³r dr == where a =.

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Q: Draw the graph of y = 3x2 + 6x − 24 and label its minimum

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, the total…

A: We have to find value of area AL

Q: The cylindrical shell method is to be used to compute the volume of the solid generated by revolving…

A: Here, the region bounded by the curves y=2x-x2, y=0 is rotated about the line x=3 as shown in the…

Q: fx,> 8 and x n+1 2 for n EN. Then the limit of x is equal to X 21 ......

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Q: 5. f(x) = e³x-5 6.f(x) = (1 + cos x)8

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Q: Evaluate the following double integral over the given region R. SS 4 ln(y + 1) (x + 1)(y + 1) Use…

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

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Q: y = (x²-2x) (In x³-3 tan x) x√x

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Q: A B B + A Bx + + I A Т Identify the form of the partial fraction decomposition of the rational…

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Q: The value of $ (2xy - x²)dx+ (x+y²)dy, where C is the enclosed curve of the region bounded by y=x²…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   I=∮2xy-x2dx+x+y2dy And C: y=x2, y2=x…

Q: 4. (a) Find (b) Hence evaluate d dx √1+x² X S (1+x²)³/2 dx.

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Q: uestion 12 The power series representation of f (x) = ln(x2 – 1) is given by A. None of the choices…

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Q: Consider the region on the 1st quadrant bounded by y = √4x², x and y - axes. If the region is…

A: Solution is here

Q: 3x at the point P (2,0, -1) in the direction The directional derivative of f (x,y,z)=ln *(x,y,z);…

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Q: Consider the region on the 1st quadrant bounded by y = √√4 — x²,x and y - axes. If the region is…

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Q: Find two numbers whose sum is a, if the product of the square of one by the cube of the other is to…

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Q: Find O does not exist O-1/2 00 01 D 01/2 O Other e-1-1

A: We have to find the limit

Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: lim [(x²-In(x + 1)) cot x] x-0-

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Q: 2x f²f²² (x² + 2y³) dy dx. Write the iterated integral in the previous item using the order dx dy.

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Q: 8² 8²v 8² = (x² + y² +2²) −¹, then + + is 822 მ2 If v=

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Q: 5 Given cos(8)= and the terminal side of 0 lies on the fourth quadrant. What is the value of cos 05…

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Q: consider using rational

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Q: Find the volume of the parallelepiped determined by the vectors (0, 4, 5), (2, 0, 5), and (-1, 3,…

A: Volume of parallepiped is (a X b).c

Q: Given the hyperbola 2² - 4y² + 2x +32y-27= 0. Find the vertices of the hyperbola. O a. NONE OF THESE…

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Q: Let f (a, b, c) = cos (ab) + sin (b) + c where f ¹ ((1/5,²)) af 1 T Evaluate да 23 π T√3 12 3 Option…

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

Q: 1. The integral can be rewritten as биз S= du u + 1 6u² S₁ -du u²+ 1 6u5 S; u³+1 f247du B. C. D. -du…

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Q: - Given the function f(x, y, z) = x ln(1 – z) + and simplify your answers. a) fa b) sin(x - 1) 2y…

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Q: The height and radius, respectively, of a cylindrical tank is 5 m and 2 m. If the tank is full of…

A: Given