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Q: 5. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then, Area region = [*f(x) dx + [[g(x)…

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Q: 13. Water is spilling out of a tank with a leak at the bottom. After t hours, there are t+ √t liters…

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Q: 2. S 2 tan x secx - tan x d.r

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Q: y"+y' = 0; y(0) = 0, y'(0) = 1 cost + sint t + cost + sint O B) 1- e-t t-e-t OA) OD)

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Q: R(t) = [(el-1, 1-², In (2-1) In(2-t)), (t,0, t - 1), if -1 < t <1 if t ≥ 1.

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

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Q: Find all points on the curve y = x3 + 2x2 -6x +5 where is the tangent is parallel to the line 2x + y…

A: The given curve y=x3+2x2-6x+5

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: Solution is given below:

Q: fx ln x dx.

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A: Use volume of solid of revolution formula for finding the volume

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

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Q: For the following homogeneous differential equation, given that y1(x) = ex is a solution, find the…

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Q: Evaluate d³yd¹y + dx5 dx4 - 6 d³ y dx³ = 0 =

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Q: ocery owner raises the prices of his goods by 10%. Then he starts his Christmas sale ffering the…

A: Given query is to find discount percentage.

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The x-coordinate of the centroid of the…

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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: indly provide a sign table with its conclusion of the curve sketching. (Concave up/ down, increasing…

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Q: evaluate * √2 2 dw √11+10w-w² O = -0.7973 O=-11.574 = -0.7297 One Hand on Pen, Other on Phone, One…

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Q: a.) [ sec²(t − 1) dt b.) 2 √t c.) [ sin(Int)

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Q: If R is the disc with center at the origin and radius 5 then the numerical value of [xdA is equal to…

A: Please follow the next step.

Q: 1 The volume of y = (3x+1)+,x=0, x=8,y=0 O (28/9) T O (26/3) T (1372/9) π O (248/9) T

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

A: Using disc method, find value of a+b+f(1)

Q: The series representation of f(x) = n(x²-1) is given by power OA ¹+¹, -1<x<1. n=] } + [ B. None of…

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Q: Choose among the following suitable to define the given integrations: * f(x + 1) sinx dx Not…

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Q: Find lim 2-0 -x-1 x²

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Q: Find the critical points of f(x) = x³ - 24x² + 144x and use the Second Derivative Test (if possible)…

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

Q: Find dy dx : y = arctan 2+1 x-1 at x = 1

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

A: Solution is given below:

Q: 3 2. Find the area bounded by the two curves y = x = x³- 6x²+ 8x and y = x² - 4x.

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Q: Which of the following equations can be derived from the partial fraction decomposition of a…

A: We can solve this problem as follows:

Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: 3. 4. x= F7 ←x=1 20

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Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

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Q: S (3-√5x) dx √7x

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Q: Consider the following sequences n In (1+n) (ž) e^/(n²+1), (iii) n²+2n - 11. Which of the above…

A: We have to check which sequence is monotonic increasing.

Q: The face of the gate of a dam is in the shape of an isosceles triangle 4-m wide at the top and 3-m…

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

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

A: To find the two numbers whose sum is 'a', if the product of the square of one by the cube of the…

Q: Let y = = 1/2 √ √x. Then evx dy dx is:

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Q: Find -3) 2/2 lim xxx+1,

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [₁ f(x) dx + ["40 + [~…

A: Here in this question, three curves are given and we need to find out the limits of integration, and…

Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: 4. x = 3 + 4 sine, y = 3cos0 - 4

A: Given: x=3+4sinθ, y=3cosθ-4 dxdθ=ddθ3+4sinθ = 4cosθ dydθ=ddθ3cosθ-4 = -3sinθ

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: Simplify: 1 1 + csc(0) + cot(e) csc(0) - cot(e) A 2sin(e) B 2 sin(8) 2 sin(8)

A: 1csc(θ)+cot(θ)+1csc(θ)-cot(θ)=csc(θ)-cot(θ)+csc(θ)+cot(θ)csc(θ)+cot(θ)csc(θ)-cot(θ)

Q: In the partial fraction decomposition for some numbers A, B, and C. Find the value of B? -x²-x+2 C A…

A: On solving this we will get:  B= 1/2

Q: f ƒ (a,b, c) = cos (ab) + sin (b) + c where ƒ ((2, 73,7)) Evaluate af да (1,3,7) O Option 3 T√3 12 ل…

A: Topic:- application of partial derivatives

Q: Evaluate z' if z = [1 + (x² − 1)³] ²³ O a. 2(2²-1)² (1+(2²_1)²³) i O b. none of these О с 41(2²-1)²…

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Q: Consider a point in Cartesian coordinates given by (3√3, -3, -8). Find a corresponding spherical…

A: Solve the following