Which of the formulas below will give the area of the region enclosed by the polar equation r = 4 sin 0? S/² (4 sin 0)² de (4 sin 0)² de Option 2 16 5/² sin²0de Option 1 8 for sin² ede

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

A: We first sketch the given region using a graphing calculator.  We will consider the graphs about…

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

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Q: 12 The value of the definite integral fm1² √ex – 9 dx is in the form F (b) – F (a), where a 19 and b…

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Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: 2x² + x³ 3x² + 4x-9 1² +1 Q(x) + p(x) 1²+1

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

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Q: The numerical value of the lim n+3 nln (2) "→ ∞ \ 11 + 1 is equal to

A: We need to evaluate the value of the following limit limn→∞n+3n+1nln2 Formula Used: limx→∞1+axx = ea

Q: Which ONE of the following statements is TRUE with regards to lim (x,y) → (0,0) sin (xy) x² + y²

A: The correct answer is option D.

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

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Q: Part I: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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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

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Q: 12

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Q: stion 12 The power series representation of f(x) = ln(x²-1) is given by OA. None of the choices in…

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Q: The integral can be rewritten as 6u³ (a). [√ 小 1+1 6u4 (c). Su u² + 1 - du du dx √x + √x S 6u² u² +…

A: Given:       ∫dxx3+x     Prepare for substitution:        =∫16x56·6xx6+1dx  substitute…

Q: fy = √2 – 3x², find d'y dr2

A: Given query is to find the Indicated derivative.

Q: X -S²- VO- The numerical value of dx will be equal to

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Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0 using a vertical element

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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…

A: Given problem:-

Q: tex Given; ·S= dx 2 Applying rationalizing substitution, find dx in terms of z. (2 z + z) dz A z² z…

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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…

A: The integration of the integral is 1/[x^(1/3)+x^(1/2)].

Q: The volume for solid of revolution between curves is the volume of the object between a curve f(x)…

A: We have to find the volume.

Q: - Find the value of x of which the function f(x) = O a. none of these O b. 1 OC -1 O d. -3 Oe. 3 2-8…

A: Given:f(x)=12x-8

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

A: Let's compute value of given a+b+c+d-4f(2)/g(2).

Q: dx Evaluate ·S= using rationalizing substitution. x1/2 + x2/3 (A) none of the choices B 6 In (x1/6)…

A: The integration of the integral is  1/(x1/2+x1/3).

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

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Q: Find and classify all critical points of the function f(x, y) = x + 2y - ln(x4y8) Item 5.pdf

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

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Q: x-y SS² dA over a square region Using the transformations u=x-y and v=x+y to evaluate Rx+y with…

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Q: A rectangular plate is submerged in water as shown below. The top of the blue region is the surface…

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

A: Volume of solid revolving about x axis  between curves h(x) and f(x) is given by

Q: PART II: What is the area bounded by the curve y² = x and the line x - 4 = 0?

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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: Evaluate the following integrals: (a) [*[**cos(2) dx dy VI- b) √ √²²- e−2²−² dy dx (Hint: Use polar…

A: We have to find the given double integral. (a) The given integral is…

Q: A biodiversity organization releases 1200 tilapia into a lake. After a year, there are 2000 tilapia…

A: Let's find growth logistics model.

Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: Here we have to find the value of r and then plot the polar graph.

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: what is the final answer? can you write the final answer in 7/6 leters/min?????????? whats that?

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Q: Pleaase help me in my subject Calculus   The volume for solid revolution between the curves y =…

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Q: 4ex. Given: v dx 2 Applying rationalizing substitution, find dx in terms of z. 2 z dz A z²+2 (2z+z)…

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

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

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: Given: 4x+8y=8, y=0 x-axis, x=0 y-axis So, the bounded region is as shown below. Apply the disk…

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

A: Given

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 the Critical points of the ff equation and Determine the Maximum and Minimum. - 1. y= 2x² - 12x…

A: A detailed solution is given below.

Q: If A = {x+|x-1| : xER}, then which of ONE the following statements is TRUE? A. Set A has a supremum…

A: The set A=x+x-1: x∈ℝ

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = S [² f(x) dx + √° 9( g(x)…

A: Given the region is bounded by y = x3 , y = 2x+4 and y = -1. Intersection of y = x3 and y = 2x+4 is…

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: We need to find volume.