Evaluate the moment M, and My of the region bounded by x- 2y - y? and the y-axis.

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

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A: We can find the integration as below.

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A: Since you have asked multiple questions in a single request we would be answering only the first que...

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Q: triple integral of  3xy dV, where E lies under the plane z = 1 + x + y and above the region in the ...

A: Let's find. 

Q: If g(x) = | sinx dx and g |=3, then g (0) is equal to 2 A -2 B 4 D 2.

A: We can solve this as follows:

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A: Given y = -2x + 5

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A: First we find singular points.  Follow step 2,3 . 

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Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

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Q: Find all points c satisfying the conclusion of the MVT for the given function and interval. y = V3 c...

A: Here, the given function is: y=f(x)=3cos(x)-sin(x), [0,2π] Here, f'(x)=3(-sin x)-cos x=-3sin x-cos x...

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Q: 6. Evaluate the following indefinite integral as an infinite series. sin x (a) (-1)". 2n+1 (b) (-1)"...

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A: To evaluate the given integral.

Q: Hiw.r provethat D2f +32f= y=o far the functionel xe -2y Coos 2X %3D

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Q: Find the antiderivative, G(t), of the function g(t) = (3n?t? – t4)V3n² – t².

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Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

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Q: Identify and sketch the surface of each of the following 4 equations. Label the intercepts and trace...

A: Identify and sketch the surface of the following equations1. 4x2-3y2-2z2=02. 25x2-100y2+16z2=-400

Q: Beginning 29 miles directly north of the city of Hartville, a boat travels due east. The boat is tra...

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Q: Solve the Lagrange's partial differential equation 2 z* p – xy(x² + yz)q = xz(x² + yz). 4

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Q: dx -2 (5-4x- x²)2

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A:   ---------------------------------------------------------------- x2+y2-6ax=0                     ...

Q: Consider 5 a8 +2 x2 +2 sin(x)–2 f(x) = %3D -28+5 x+5 Find the behaviour of f(x) as x → oo. • If lim ...

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Q: Evaluate f(cos4 x – sin“ x)dx

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Q: Consider the fünction: f(x) = 5x + 15x² - 5x- 3 %3D Step 1 of 2: Determine the intervals on which th...

A: Concave up if f"(x)>0 Concave down if f"(x)<0

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Q: Find the volume of the solid generated of the area bounded by y? = 8x and y = 2x, rotated about y = ...

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

Q: Find the indicated derivative for each of the following functions and evaluate as indicated: A. f(x)...

A: Take the derivative using power rule of derivative then substitute the value of x and simplify. 

Q: Find the volume generated by revolving bout the line x = 3 the area bounded by (y – 2)° = -4(x – 4) ...

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Q: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint ...(1)y=1-sintdydt=-c...

Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y...

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Q: se the Root Test to determine if the series (-1)" 2/n en² (2n2 – 1)" CONVERGES - n=1 converges or di...

A: As you have asked for the solutions of question number 3 only. So I am solving only that. Hope it he...

Q: 5. S Vr3 In(Vx) dx 6. Si, Inx dx J1

A: This question is based on indefinite and definite integral.

Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: Evaluate f(cos“ x – sin* x)dx

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Q: Problem 6 (1-cos2x)+2cos²x S V2x + 1 x² dx

A: Solved below

Q: Use the areas shown in the figure below to find the following. y = f(x) Area =0.7 Area =15 a Area =2...

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