3. Evaluate the following using Integration by Parts, Algebraic Substitution, Trigonometric Substitution or Definite Integrals a. Sxe2*dx dx b. S xV4+25x² c. S(5x – 1)Vx + 2dx

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A: ∑n=1∞23n(n!)3(3n!) For ratio test, L=limn→∞an+1an

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A: Here ,we have given a definite integral.Now we solve it by using rules of integration. Then we put…

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Q: Evaluate e |/| 2xz dV where E = {(x, y, z) | 0 < z < 1, ¤ < y < 2x, 0 < z < z + 3y} E Round your…

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Q: Determine the area of the region enclosed by the curve y = x2 – 2 and line y=2

A: Given that y=x2-2 and y=2To determine the area enclosed by the curve.Solution:

Q: 8.) y Inxlny dx + dy = 0

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Q: 2. Use the fundamental theorem of calculus part 2 to compute the integral 1° dr. 0,

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Q: r'dA D = {(x, y) : 1 <I<e, 0Sys In(r)}

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Q: Find all solutions of the system of equations. (If there is no solution, enter NO SOLUTION.) 7. 9 =…

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Q: Bradley has 35 baseball cards. H shared them equally among himself and 6 friends. Then Bradley…

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Q: 3 Simplify cos(arctan2). √5/5 no solution 2√5/5

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Q: 5dz (z+4)Vz+1

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Q: Evaluate/Find the following integrals. 2 4. S2-3 3 -dy 1 У +у 2

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Q: Your explanation should answer WHY you are doing the work and HOW you are doing the work briefly…

A: If f'x is:→ then fx is-ve→decreasing0→horizontal +ve→increasing=a &amp; ≠0 →slant with slope…

Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: Find the principal value of arcsin . 30° 60° no solution

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Q: JI (x - 1)5 + 3 (х — 1)? + 5 Jdx

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Q: Determine if the following statement is true or false. The lines L and L2 are skew. L:x= -1+2t, y =…

A: The given lines are: L1:x=-1+2t,y=10+3t,z=2-tL2:x=-7-5t,y=1,z=5+4t Here, the normal vector of the…

Q: a) A small metal bar, whose initial temperature was 10° C, is dropped into a large container of…

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Q: (k) (In n)n n> 2.

A: k. 1ln nn ,  n≥2let, un=1ln nnun=1ln nn12=1ln nn2by cauchy roots testlimn→∞  un1n=limn→∞  1ln…

Q: The lower edge of a mural, 12 feet high, is 6 feet above the observer's eyes. Under the assumption…

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Q: etermine the area of the region bounded by the curve y = -x2 and y=x.

A: solving both the curvesy=-x2 and y=x-x2=xx2+x=0x(x+1)=0x=0,-1at x=0, y=0at x=-1, y=-1Lower limit…

Q: State whether each of the following series converges absolutely, conditionally, or not at all. n²…

A: A series ∑an is called absolutely convergent if ∑ an is convergent . Limit Comparison Test :   If…

Q: Find the total area of the shaded regions. y=x√(36+x^2)

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Q: Determine whether each improper integral below converges or diverges. dx 3. S. x* + 2x – 3

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Q: dy 1+ y+1

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Q: 2t dt Vel +3

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Q: x*-6x³+e* Vx dx

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Q: (a) P:4x-3y-6z-2 0 P2:-12r+9v+ 18z-5=0 O Parallel O Perpendicular O Neither eTextbook and Media Hint…

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Q: 1.What are the possible values for f"(x) if f"(x) exists and Ax,) > Ax,) for every x1 0 c. f'(x) =…

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Q: Integrate: (7x³ + 4x²) dx

A: Given:- ∫(7x3+4x2)dx

Q: ((- +3) dt 21.

A: the given integration,       ∫0245t3-34t2+25t dt

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: Given, f(x)= 5x2/3 [-1,1] Finding the critical points we have, f'(x)= 5(2/3)x(2/3)-1 f'(x)= 10/3x1/3

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Q: Given the area in the first quadrant bounded by x2 = 8y, the line y – 2 = 0 and the y-axis. What is…

A: Given the area in the first quadrant bounded by x^2 = 8y, the line y – 2 = 0 and the y-axis. Find…

Q: 7) Find the radius of convergence and interval of convergence of the following series: (х — 2)" | n²…

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Q: Evaluate/Find the following integrals. 1 dx 3. S- 3 1+ x

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Q: %3D Click on the graph below to choose the graph of the function "arccot (x)." 3

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Q: Consider the points A(3, –3, 3), B(4, –5, 1), C(-2, -4, 1), and D(6,3, –5). |(a) Find the volume of…

A: Let's find.

Q: b. f(x) = x - 3 x² – 9 2-

A: The given function is,   f(x)=x-3x2-9

Q: Choose the values that would complete the general solution for y = arcsin ( - 3). _±2¤k 3 O O O

A: Solve for the value of y.

Q: Determine if the following statement is true or false. The lines L1 and L2 are skew. L:x = 10 + 3t,…

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Q: 7 dx 5. S 2 2 3 xVx-4

A: We will solve the integration.