1. Find the Inverse Laplace Transforms of the following. 3s 2), 35544 2

Q: (1+y^2)dx+(x^2y+y+2xy)dy=0

A: 1+y2 dx+x2y+y+2xy dy=0

Q: •π * (sin³ x)√1 + cos x dx 2

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Q: A) Match each equality with the letter corresponding to the property it illustrates. Responses may…

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Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

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Q: Find the point on the line y = 8x closest to the point (1,0). (Use symbolic notation and fractions…

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Q: CONSIDER A FUNCTION OF R IN R DEFINED BY: x² + 1 X-2 SO, THE EXPRESSION: f(x) - f(3) x - 3 FOR 2 IS…

A: f is a function of R in R defined by  f(x)=( x2+1)/(x-2)  Then expression [ f(x)-f(3)]/(x-3) ?

Q: Evaluate: ³₂(4x²y - 2³) dz dy dx

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Q: Let R be the region below bounded by the graphs of C₁: x² + y² = 16, C₂: y = 4 − (x + 2)², and C3: y…

A: If you have any doubt feel free to ask.

Q: Evaluate the integral: S/2 sin(4t - u) du dt

A: The integration of the double integral is Sin(4t-u), u from 0 to t, t from pi/2 to pi.

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

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Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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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: y = 1 1+ u 1 1-x

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Q: What is the equation of the tangent line to the curve y = at point (0, 0)? O none of the choices O y…

A: Given :      y = 3√x    Point : (0 ,0)

Q: The value of √x dx 1+ A. x-2√x+2 ln (1+√√x) + C B. x-2√x-2 ln (1 + √√x) + C C. x-2√x+2 ln (1+√√x) -…

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Q: he first term of an anthmetic sequence is 6, and the tenth term is 2. (a) Find the common difference…

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Q: Ex. Find the general solution to dy 1 -2.x dx X -

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Q: Evaluate the following * [csc² cot (5x+6)/2 + C cot(5x+6)/ 5+ C - cot(5x+6)/ 5+ C cot(5x-6)/ 5+ C…

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Q: Evaluate the integral: 2 So sin(4t - u) du dt

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Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 4 12 y² +1

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Q: Let R be the region enclosed by the polar curve r (0) = 3 ln (0) where 7π <O< 8 Y X 72 ㅠ R 1 1

A: Given Curve rθ=3ln(θ)whereπ2≤θ≤7π8

Q: Given the following graph of f(x) , use your understanding of derivatives to sketch a graph of f'(x)

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Q: 3 If the total cost function is given by TC = 300+5g + then the marginal cost function MC = I 3 O a.…

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Q: Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the…

A: A critical number of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Find the dimensions of the rectangle of maximum area that can be formed from a 10-m piece of wire.…

A: We have to find the dimensions of the rectangle of maximum area that can be formed from a 10-m piece…

Q: Find the volume of the solid generated by revolving 1 the region bounded by y = e¯x², the x-axis and…

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Q: The value of sin cos (x²+)+C C. cos (x²+)+C xp B. -cos (x²+)+C D. -cos (x²+)+C

A: Topic = Integration Correct option = B

Q: 11.Doe = 8. Find the slope of the secant line. f(x) x-8 3x+4 X1 = 2, X₂ = 0

A: Here we have to find the slope of a secant line.

Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Evaluate the integral: -2e π/3 ₁²/³ tlnu tans ds du dt

A: Topic = Integration

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

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Q: t = b? Choose 1 answer: b Ⓒ / ° v A a © B Ⓒ a b cb a a b e20t+t6 dt e10t+t³ dt 10e10t+ 3t² dt…

A: Topic = Integration

Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

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

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Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

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Q: Suppose ƒ(x) = 2¹². What is the lim ƒ(x)? 700 O A. It is a vertical asymptote of f. OB. It is a…

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Q: -3 ³₁₂₁(4x²y - z³) dz dy dx

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Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

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: What is the direction of the vector with an initial point of (3,-5) and a terminal point of (8, 6)?…

A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: (2) Z/(5) =....... (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find the operation

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

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Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

Q: Evaluate: ƒ²₁ ³² ²₁ 0 [(x²-y²)²] x+y du de

A: Follow the procedure given below.

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

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

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Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

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Q: NO PARKING See Se THIS BLOCK 2AM 5AM STREET ARLING 2 HOUR PARKING THIS BLOCK 9AM 6PM EXCEPT SUNDAYS…

A: Solution