For x>0, differentiate the function g(x) defined by eg(x)= xe-2x, The required derivative is g'(x) =

Q: S(curl F) · n dS  where F  =  4yz i  +  6x j  + 5yze x2 k  , S is the portion of the paraboloid  z…

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Q: The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one…

A: Given that the Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission…

Q: 10. Let X and Y be topological spaces. Show that if either X or Y is con- tractible, then every…

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Q: 2) Write the negation of: VxER, 3 € Rǝ x² + y² > 0.

A: We know that negation of "for all " is "there exists" and vice-versa. And negation of 'greater than…

Q: THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . , then L{t¹f(t)} =…

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Q: realizes that she hasn't reset her pedometer. From the Chupacabra Tr es along a bearing of N41°W…

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Q: Problem #1: Problem #1: Use Stokes' Theorem to evaluate F F dr where F = (x + 7z)i + (3x+y)j +…

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Q: f is a function with the following Fourier coefficients on the interval [-] Jag=0 a₁ = 0b₁ = | 0b₂ =…

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Q: Solve the initial value problem d²y dt² Select one: O& Ob Od - dy + y(t) = et; y(0) = 2, y'(0) = −1…

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Q: A₁ = [1₂8], 0 [:)], 1 A3 = A₂ A4 = - [8], - [89] 1 2x2 form a basis for the linear space V = R²×2.…

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Q: The cost of manufacturing a toasters in one day is given by C(x) = 0.07x² + 18x + 350, 0 < x < 150.…

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Q: Consider the function f(x) = sin (x7). a. Differentiate the Taylor series alfout 0 for f(x). b.…

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Q: Use the divergence theorem to write a triple integral that is equivalent to the flux integral - = 64…

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Q: Fins the area bound by one pedal of the rose curve f(theta)=4sin(3theta)

A: The given problem is to find the area bounded by one pedal of the rose the curve…

Q: a. C. 2 1²2 [132] 0 b. 2 d. -2-1

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Q: Evaluate B (xy + yz + xz)dV B {(x, y, z) | 0 ≤ x ≤ 10,0 ≤ y ≤ 10,0 ≤ z <10}.

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Q: e general solution to y" - y' + (81x¹ −72) y = 0. X

A: Given    y''-5xy'+81x4-72x2y=0  Here we use the formulas:  to find Integrating Factor(I.F)=e∫P(x)dx…

Q: 1) Let f(x) = 1 + 2x³ - x and g(x) = 2x + b, for xeR, where b is a constant. a) Find (gof)(x). b)…

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Q: Evaluate the below integral by making the given substitution. Use C for the constant of integration.…

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Q: (a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z²k through…

A: Given, F→(x,y,z) = z2k→The surface is the upper hemisphere of  x2+y2+z2=25.

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Q: Use Stokes' theorem to write a line integral that is equal to the surface integral curl F. ds, where…

A: By stokes theorem                            ∫∫s ∇×F→ ds =∮F.→ dr→  we have evaluation of Line…

Q: Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value…

A: x''''-5x''+4x=sint  with initial condition x0=0, x'0=1, x''0=0, x'''0=0

Q: Objective Function Maximize: Z = 30X₁ + 50X2 Subject to: Constraint 1: 2X₁ + X₂ ≤ 16 Constraint 2:…

A: In the given problem a linear programming problem is given. We have to find the value of the…

Q: Solve the initial value problem below using the method of Laplace transforms. y"-3y'-18y = 0, y(0) =…

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Q: Use the divergence theorem to write a triple integral that is equivalent to the flux integral S = 64…

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Q: solve the initial value problem   xy' + 4y = 3x^2, y(2) = 4

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Q: Suppose that P2(x) = a +bx+ca² is the second degree Taylor polynomial for the function f about x =…

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Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: ƒ : R → Z via f(x) = x²-10 5

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Q: The following are the results of a series of bicarbonate determinations (mmol/L) run in September…

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Q: Question 3 Consider a system with differential equation given by d³y d'y + dt³ dt² dy dt -y=e^t. a)…

A: Given : A system with following differential equation : d3ydt3 + d2ydt2 - dydt - y = e-t

Q: 4/5 divided 1/4

A: 4/5 divided 1/4

Q: Select the partial differential equation that can be used to model this scenario. J²u Ju A.k- dz² B.…

A: A String of length L is secured at both ends. The string is released from rest with initial…

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Q: 2z Sc (2²+273 dz (z-w)³

A: CAUCHY THEOREM-: IF F(z) IS AN ANALYTIC FUNCTION IN A SIMPLY CONNECTED REGION ,THEN ∫cF(z)dz=0 ,…

Q: 6) Respond to each of the following. a) Find 1010112 + 110112 b) Write 1001010₂ in decimal form. c)…

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Q: Determine the solution of the following differential equations:

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Q: 2. For which of the following series does the ratio test ensure divergence? Select all that apply.…

A: Let ∑un be a series of positive real numbers and let limn→∞un+1un=l Then ∑un is convergent  if…

Q: 4. List all solutions in polar form of the equation x5 = 3 in the complex numbers. (Start by finding…

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Q: Calculate fff(x, y, z) dS For s f(x, y, z) ds = = x² + y² = 9, 0≤ z ≤ 4; f(x, y, z) = e¯²

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Q: Consider the function f(z)= |z|2 defined for all z ∈ C. Answer whether the following statement is…

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Q: e Lay xy¹ ds where C' is the right half of the circle x² + y² = 9 Evaluate

A: We find required integral by parametrizing x and y .

Q: (b) xy' + 3y = 4x, y(2) = 6

A: This is a problem on differential equation of first order. We have find an Integrating factor then…

Q: ZD Sdz edz,

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Q: b a C c and d b and c b and d d and f e and f a and b c and f f d e elect all pairs of vertices…

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Q: 3. (Section 17.6, 17.8) Consider S₁x² + y² = 9, S₂: z=0, (a) Graph surface S. = xî + yĵ+ (2² − 1)k.…

A: The given function is F=xi^+yj^+z2-1k^, and the Surface S is bounded by the surfaces S1:=x2+y2=9,…

Q: Using Delta Epsilon Proof sin x 2. Prove: lim x-0 1.

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Q: Evaluate the surface integral. [6 ( ² + x²y) ds S is the part of the cylinder y2 + z² = 9 that lies…

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