1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y = 2 2 3y + 3z = 3

Q: 2 t √3u Evaluate the integral: №³4 524 4²2 ds du dt s²+u²

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Q: What is the lim 700 (n-1)-1 + (n − 2) x^²-2 +...+ OB. undefined O.D. 22-1 ne2+7

A: Here, to evaluate: limx→∞xn+xn-1+xn-2+...+x(n-1)xn-1+(n-2)xn-2+...+x

Q: f(x, y) = ln(x² – 25) + √√-y² - x² – 10x . -

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Q: x 1 4. 1 / ₁²+52²+8² dx x² + 5x + 8

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Q: -2 -t² rln s Evaluate the integral: 5² 5²² n fote" du ds dt

A: We have to evaluate the integral ∫12∫tt2∫0ln st eu du ds dt.

Q: Show that (x+2)² = ln(x + 2) - x+2 + C.

A: Topic = Integration

Q: 2. I. -4 1 Evaluate each determinant. 3 -3

A: -431-3=12-3

Q: 312-3x| dx

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Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: 2. Evaluate all of the integrals. r² sin r dr

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: Evaluate: 3₂₁ [2³(x + y)³] dz dy dx

A: Given: I=∫-23∫-12∫01z3x+y3dzdydx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C, where a &…

Q: Evaluate: ³₁₂₁(4x²y — z³) dz dy dx

A: The given integral is  ∫-13 ∫-24 ∫10 4x2y-z3dz dy dx

Q: 1. Evaluate the assigned limit using L'Hopital's Rule. lim [cos (2x)]¹/(*-*) X-T

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Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: he table of integrals to evaluate the integral. (Use C for the constant of integration.) sin (20) J…

A: The solution is given below.

Q: y' = xy2 O y(x? + c) -2=0 2 (x² + y=(x+ c) + 2 = 0 y(x= + c) + 2 = 0 y2(x? + c) + 2 = 0 00 Ꮎ

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Q: S √16 - x² dx X 4+16x2 A)√16-x2 - 4 In X C) √/16 - x² - sin-1 ] + c - C B)√16-x2+4 In 4+√16-x2 x2…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 5. I. Evaluate each determinant. -2 -1 4 2 5

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Q: Whatis the equation of the line that passes through (-3,5) and is parallel to theline 4x - 2y + 2 =…

A: The line passing through -3,5 and parallel to the line 4x-2y+2=0

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Area under curve

Q: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Find the area of the region bounded by x= 1/(y2+1) and the y-axis using the horizontal strip.

Q: S √x²-25 dx X

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Q: - Let v and w be vectors such that |v| = 2, ww = 36 and the angle between v and w is T/3. Calculate…

A: This question can be solved using the concept of vectors.

Q: Evaluate the integral: So So So 2 rt c√3u 0 0 น s²+u² ds du dt

A: Given problem:-

Q: (x²-y²)²1 Evaluate: ₁²² du du dt x+y

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Q: Write z₁ and 22 in polar form. (Express 0 in radians. Let 0 ≤ 0 < 2π.) Z₁ = 2√√3 - 21, Z₂ = −1 + i…

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Q: 1. 3 If the total cost function is given by TC = 300 +5q+ what is the marginal cost when q = 3? q² 1…

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Q: se local linear approximation to estimate In (0.99).

A: topic- linearization of a function

Q: A third-order differential equation has a general solution of: y=e-2x(C₁ + C₂cos8x + C2sin8x).…

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Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

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Q: ng a trig substitation, the integral (A) / sec(0) do dr can be transformed into one of the

A: Please refer to the image below

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: Sy² sin Sy dy 1 A) ----² cos Sv + y sin y sin Sy + 1 256 32- 1 1 B) ² cos By-y sin Sy-256 9-11-² sin…

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Q: Evaluate: ₂(4x²y - z³) dz dy dx

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Q: y"" - 4y" + 3y = 0

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Q: II. Use the difference table to predict the next term in the sequence. Show your complete formula.…

A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: I. 1.) Simplify. Write "undefined" for expressions that are undefined. 2 [164] -6 -5

A: Topic = Matrix

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: = 2 · and g(x) = √x² – 2x +1, then_lim [(ƒ(x) · g(x)] is z→1¹ If f(x) =

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Q: √ (2x - 7)6 12 (2x + 7)- 12 (2x - 7)5 + C + C (2x - 7)-6 12 (2x + 7)6 12 - + C - + C

A: Topic = Integration

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: 2. Evaluate all of the integrals. x²-x+4 (x+1) (x²+2) da

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Q: -3 Evaluate the integral: ³ ft t² et du dt

A: We know, ∫emxdx=emxm , for any real number m. ∫xndx=xn+1n+1, for any real number n.

Q: If lim f(x) = -∞, then which of the following is TRUE? I-0 O None of these. Ox= = 0 is a vertical…

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Q: (5) If f(x) =........., then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

A: This is a problem related to reducible and irreducible nature of the polynomial while in Z5[x].…

Q: Evaluate the integral: t² ls teu du ds dt

A: Let's evaluate given triple integral.  There is no need to draw the graph.