Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 16 + x²-y² R = {(x, y): x² + y² s 4}

Q: Solve the following differential equation using Laplace transform 1. dx2 d²y + 25y = 10 (cos(5t) – 2…

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Q: 4. csc 2x cx

A: The integration of the integral is csc52x.

Q: 1. Get the first derivative f': 2. Find the factors: 3. Find the critical numbers: 4. Get the second…

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Q: A company produces a special new type of TV. The company has fixed costs of $486,000, and it costs…

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Q: Find the FIFTH DERIVATIVE Given: f (t)

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Q: 09. lim, " -т(csc Tх) (Inx)| x)(Inx)]

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Solve the equation: (4D4 – 4D³ – 23D² + 12D + 36) y = 0 O y = cje* + c2xe2" + c3e¯7 + c4xe¯i O y…

A: The given equation is: (4D4-4D3-23D2+12D+36)y=0...(1)

Q: Find the common elrea between Y=2CI+Cose) and carved V=Z(1-Sine) which is Losatel in the funrth…

A: Let's find common area between given two curves. Common area in fourth quadrant.

Q: Problems for Accumulation: 2. Accumulate P20,000 for 3 years at 7% simple interest.

A: A detailed solution is given below.

Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0 %3D

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Q: 5. Solve the equation: (D² – 3D + 2) y = 2r² + 1 O y = cje* + c2e²« + 4x + 3x² + x³ O y = cje" +…

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Q: Water is pouring into a swimming pool. After t hours, there are 2t – vt gallons in the pool. At what…

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Q: A. Given f(x) = x³ - 4x2- 4x + 16, find; a. Zeros of the function b. Critical numbers c. local…

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Q: Find S(-3e-3t + Vt)dt

A: Basic integration formulas are used. I have stated the used formulas in the solution.

Q: 8. If y = (x* +2x²)e2* determine an expansion for y(5). %3D [y(5) = e2x24(2x³ + 19x² + 50x + 35)]

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Q: Solve the following by using Higher-Order Diffential Equations-Homogenous Linear Equations with…

A: Given that     (D5+D4-7D3-11D2-8D-12)y = 0

Q: If f(x) = 5x² In(6x), then f'(x) = f''(x) = f'''(x) f(4) (x) = f (5) (x)

A: We have to find derivative of give function.

Q: 5. Find an expression for y4) if y =e-'sin t.

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Q: 7. Evaluate the following: (2x2y 2+2y)dy dx A. 3.0 B. 5.4 С. 2.3 D. 4.9

A: Given query is to find the value of the integral.

Q: (3x-2) dx f x²+ 2x + 15

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Q: 4 2 -3 -2 -1 1 2 (b) Find the exact values of the numbers c that satisfy the conclusion of the Mean…

A: Let's find

Q: 1) и %3D Зх?у + xӀпу? — Inxy

A: 1.

Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Independent

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Q: 8. The general solution of y" + 4y = 3 sin 2x

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Q: ACTIVITY 2:Solve the given below. Show your complete and exact solution. 5. Given the function f(x)…

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Q: 4. If y = x cos x determine the 5th derivative. [y6) = (60x – x³) sin x+ (15x? – 60) cos x] |

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Q: ди and az ди ди Find дх ду (whenever possible) for the following functions. 1) u = 3x²y + xlny² –…

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Q: : Use PARTIAL FRACTION DECOMPOSITION to find -1 dm т2-6т-7

A: We have to find integrating using partial fraction.

Q: y" - y " -2y' = 0 O y = cje* + c2 + C3e2* O y = cje* + cze* + cze2*

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Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: 5. S 7x°csc²3x7 dx du = answer:

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Q: finfyiy-6)"dy 2. 2.

A: We have to solve given integral.

Q: x[1+ (In x) ] xp

A: This question is based on indefinite integral.

Q: 9. The general solution of y" + y = cos? x

A: Given :   y"+y=cos2x

Q: Find the Laplace Transform of the following using the definition via integration: F(t) = 5 sin 3t

A: Lf(t)=∫0∞e-st f(t) dt          =∫0∞e-st 5 sin3t dtIntegration by parts;I=5 ∫0∞e-st sin3t dt…

Q: Find the distance traveled after 6 seconds by a particle whose velocity is v(t) = (t − 2) meters at…

A: Given

Q: 1) Find a power series representation for the function and determine the interval of…

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Q: x² cotx³ cscx³ dx =

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Q: polar of a point are giv the pon R/2 R/2 6f 4 4 2 2 -6 -2 4 6 -2 -4 R/2 R/2 6. 4 4 -6 -4 2 -6 -2…

A: Topic = Geometry

Q: (メ+ッ)dx + (x4ッ)dy =。 d x dy x yz x?y

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Q: (x+1 0SxS2 f(x) = { Then what is the result of| ($2) dz 5

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Q: 6. S (10 x - 40) dx x 2 - 8 x + 15 8. S (e 5x - e 2x + 8) dx 2 e 5x 7. S 10 cot 2x dx

A: We have to find the integral.

Q: 3. Find the compound amount and interest on P1, 500 at the end of 35 years and 9 months, if the…

A: Question number 3 has been solved as per the requirement of the student.

Q: The volume for solid of revolution between the curves y = v(49- x^2) and y = 0 around the x - axis…

A: Let's find volume of solid of given curves.

Q: 5. (a) Let z = (a+ ai)(b+ bv3i) where a and b are positive real numbers. Without using a calculator,…

A: See the answer below

Q: 2. (sec 5x t C9C 5x) dx

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Q: Find the radius of convergence and interval of convergence of the series. (Enter your answer as an…

A: Let's calculate radius of convergence and interval of convergence of the given series.

Q: Solve for x. Leave answers in exact values. a) In(e**) = 25 b) 20 = 4e-2x c) eln(ax) = In e %3D

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Q: 4. Which of the following is the maximum value or the minimum value of the graph of polynomial…

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Q: I. Write T if the given statement is true with respect to the underlined term(s); otherwise, write…

A: Answer :- We have to write T if the given statement is true with respect to the underlined term ,…