1. Evaluate the integral using atrial fractions method: 3x² -dx (x − 1)(x² + x +1)

Q: Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 -dx 2 √√3x²-4

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Q: Evaluate r5/6 -π/6 2 cos 0 fo² 0 r sin Ødr de.

A: We have to evaluate ∫-π65π6∫02 cos θr sin θ dr dθ.

Q: Using double integral, the area of the region bounded by the lines y=x y=x/2 and y=2 equal :

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Q: If f(x) = lim (1+x)(1+x²) (1 + x² ) (1 + x² ).......((1+x) where [x] < 1, then - 618 1 (B) 3) (C)…

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Q: Find the solution of the following differential equation. (x² - 1) + 2y (x + 1)² dy dx 1.

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Q: the complex number z = 18 + 18j in trigonometric form Group of answer choices   19.7(cos23.96°+ ?…

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Q: 3. For the below ordinary differential equation with initial conditions, state the order and…

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Q: cln x e L L ² L the we Evaluate yez dz dx dy.

A: Given problem:-

Q: Q4: If f(x,y) = x²y +exy Siny Find 1) 2) (D = f) at po(1,0) in the direction of 0 = Po

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Q: For what values of p does the series p<3 n = 2 1 (n² In(n)) converge? (Enter your answer using…

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Q: Question 17 :S- Given : 4x - 3 A = √ (21²+8) √u²+2 ® / / / 1 (2011 B (2u²+11)u √u²+2 © ²/2 √ ( 2 u ²…

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Q: For the function f(x) 2x2, find the difference quotient 4a + 2h h 4 a²+ h 4 a + 2 h f(a+h) h f(a)

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Q: 2 9- r2-x Consider the integral fff dv = [₁² f³-²³² ²6²² + . dz dy dx. 0 S (a) Sketch the solid S.…

A: Let's solve.

Q: scalar equation of a line that goes through T(2,-5) and is perpendicular to the line 3x-6y=5

A: Equation of line

Q: Solve the differential equation dy = 1+x. dx Use the initial condition y(1) = 6. Express y in terms…

A: Given differential equation is of first order and first degree . We solve this equation using…

Q: Scotch is looking to make a larger size roll of duct tape. The current roll is shown in the photo.…

A: First finding the volume of original roll

Q: 00 country song NR6) If all of the letters in the word PENCILS are used, the number of arrangements…

A: Given ,  If all of the letters of PENCILS are used, the number of arrangement with all of the…

Q: HOMEWORK 16: Graph the following equations. 6. r = sin + 2cos² 0 7. r² = sin 20 - 3cos

A: we have to graph the given polar coordinates. let r is on x axis and theta on y axis.

Q: 300. NR4) For a graduation ceremony, there are 8 people sitting on stage in one row. If the master…

A: We want to find number of arrangement possible.

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Find the convergence set for the power series, kak O a. (-7,7) O b. {0} O c. [-7,7) O d.\mathbb {R}

A: The given series is kxk/7k.

Q: Question 3 If = 2/180°, A +C = −5 + 15j and C is the conjugate of B. Find A O 10-10j -10+10j O 3-4j…

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Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

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Q: Given: c= 8, a = 5, C = 67° C b A B C Solve the triangle. (Do not round until the final answer.…

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Q: 14 Given the triangle answer to 4 decimal places. X find the length of side x using the Law of…

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Q: 1) How many 5 digit numbers can be made using the digits 5, 6, 1, 4, 9, 3, 2 if no digits can be…

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: Find the solution by using Solution of 2nd order D-Es me x ý XỨ Tỷ - xy + y = Lnx -

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Q: 7. Determine whether the series converge and if so find its sum. (a) (b) IM8 Σ k=1 2k+1

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Q: What is this character after the 16???

A: The number is  168.  The character after 16 is 8.

Q: The hyperbola in Position I opening up opening down in Position II y² x² 4 16 1 is

A: Topic :- geometry

Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: 00 (-1) 22k+1 k! Determine whether the series converges absolutely, converges conditionally, or…

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Q: } L 1 (s? +1)(s? + 25)

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Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: 3. y= (sec ³x + tan ²x)

A: Topic:- application of derivatives

Q: √9-2³ x² + y² dy dr into a double integral in polar form. TITE f(x, y, z)dV, where f(x, y, z) = x²yz…

A: We can set up the triple integral.

Q: ·S. Given : dx. If we let the substitution =√√√4x-5, the resulting integral becomes 4x-3 (2u²+11) ^…

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Q: See

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Q: Identify the conic section whose equation in standard form is y 2 + 8y - 10y - 34 = 0. ellipse…

A: Topic = Geometry parabola

Q: - Find the volume of the region cut from cylindrical (x² + y² = 16) by the plane z 0 and the plane…

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Q: Evaluate the following determinant by using row-operations. Carefully -1 3 4 -10 -4 A -> -4 -8 9 6…

A: To find the determinant of the given matrix A.

Q: MATHS HOME A 41. If f (x) = f[ta (A) 3-e^/4 4 J'a (B). tan((nx) +- dx & f(1) = 0, then f (e/4) is -…

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Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: ㅠ y = 2sinx and y = 0 from x = 4 ㅠ to x = .

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Q: Find the center and radius of the circle whose diameter has an endpoint at (3, -4) and the origin. 5…

A: Given that the endpoints of the diameter are 3,-4 and 0,0.

Q: If lim f(z) = 2 and lim g(x) = 7, then lim[3ƒ(z) — 4g(x)] = -22 G- *-b Ⓒ True O False

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Q: log x² loga +log(xy)² +loga (*)-( log x loga xy • a, x and y are real numbers that are greater than…

A: Given that logaaxy+logaxy2+logaxy-2logxloga-alogax2Solution :logaaxy+logaxy2+logaxy-2logax-x2logaa…

Q: ·S. Given : 1 value of -AB AB. 3 72 40 8x + 1 20 3 280 3 4x - 3 4x - 3 dx. If we let the…

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Q: -1 2 (x² +1) dx

A: To evaluate: ∫x6-1x2+1dx Let I = ∫x6-1x2+1dx Using polynomial division we get  I = ∫x4-x2+1-2x2+1dx

Q: 1. (ex + lny + 7) dx + ( 85 + In x + siny) dy = 0

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