Evaluate the following definite integral leaving the result in its EXACT form by showing the integration by parts process: sin(x) In (cos(x))da

Q: Use the Laplace Transform to solve the given initial value problem. y" + 2y' + 5y = 0; y(0) = 2,…

A: The given equation is; y''+2y'+5y=0, y(0)=2, y'(0)=-4.

Q: The graph of a quadratic function with vertex (-1, 0) is shown in the figure below. Find the range…

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Q: - 1. Evaluate the x for parametric equations x = 3t² – 6t a y = 3t³ + 3t with respect to the…

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Q: Determine whether the integral is convergent or divergent. Evaluate if it is convergent. If you are…

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

Q: the Wa Salve the... Following.. ......3x³6xy Ax (3x²+2 y.).dy. =a ... ... ... ... ..x 2y.). dy...…

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Q: [3] Find dy for the curve given by: 4x -x²y³ = e5y +9y

A: We can find the derivative by using the implicit differentiation.

Q: . (tan¯¹(t),e¯² Evaluate lim (tan-¹(t), e-2t, Inty t→∞

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Q: The function f(x) = 2x³ − 33x² + 108x - 7 has two critical numbers. X = (enter the values separated…

A: Topic- Application of derivatives We are given, f(x)=2x3-33x2+108x-7we know that critical numbers…

Q: A quadratic function fis given. f(x) = x² + 6x (a) Express fin standard form. f(x) = x (x + 6) (b)…

A: GivenQuadratic function f(x)=x2+6x We need to finda. Standard form of fb. Vertex of f, x intercepts…

Q: A boat is towed toward a dock by a cable attached to a winch that stands 6 feet above the sea level.…

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Q: Find the critical numbers of the function f(x) graph. x = X = X = is ✔ Select an answer Local Max…

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Q: F(s) = - A the in 3 B 55/2 S 3 -1/2 There is no correct answer from the given choices. D √₁ given…

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Q: Find the domain of the following vector-valued functions. Š(t) = (tant, √4-t², =) 2+t

A: domain of tan t is 'all real numbers';   The domain of tan t is all real numbers except for…

Q: 2. Write the formula for area of a circle: (a) Which two variables are related by this formula? (b)…

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Q: 1. Find the five fifth roots of unity in the form a + ib

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Q: A woman walks along a straight path at a speed of 5 ft/s. A searchlight is located on the ground 24…

A: We need to find the rate of searchlight.

Q: The integral in this exercise converges. Evaluate the integral without using a table. -7 S -7 ∞ 72…

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Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = t³ – t² –…

A: Topic- Application of derivatives We are given x(t)=t3-t2-16tWe know…

Q: 1. Let x₁0 for all ne N. (a) If xn0, prove that √x -0. (b) If xn →x, prove that √√√√x.

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Q: A current state has a population of 3500. With the rate of 0.23/year, what will be the population…

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Q: H.W: Solve the following equations.... x Ben Bruden denken. . Berd... 4 X dyr X² 3.4).d.x.=.a.. T

A: 3) xy'+(1+x)y=e-x. 4)xdy+(x2-3y)dx=0.

Q: r> 0 r< 0 (4₁-2-3) (r, 0) (r, 0) = X X

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Q: (b) Find the 243rd derivative of f(x) = sin(3x) 3

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Q: x 9 PCRS (57) thenewboston YouTube A31 W6 Complete Lectures.pd C…

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Q: dz/dt is incorrect

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Q: f(x)=x²+2x-6 has an inverse g(x).. 1 ƒ'(g(x)) Use g '(x)= g'(-6)= 110 to find g '(-6).

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Q: 2. Separation of Variables Determine which of the following differential equations are separable. Do…

A: according to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Find the solution of the nonhomogeneous linear differential equation using the method of…

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Q: Use the matrices below to perform matrix multiplication. If the operation is undefined, enter NA. BD…

A: Given matrix:- B=374-9012 D=3-41284107-10

Q: 5. Expand the logarithmic expression and simplify. In e' (+1)*

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Q: -9 -8 (-inf,) -7 -6 -5 -4 -3 a. Select an x-value in the first interval, (-∞, - 2/2 ): -2 -1…

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Q: Use the matrices below to perform matrix multiplication. B = 27 3] 14 -10 0 12 || |- 4 -3 5 10 6 8

A: Number of  column in B =3 = Number of Row  in   C  so, matrix multiplication is possible

Q: Find the equation of the tangent line to the function f(x) = 2x² - x at the point where X x = -1.…

A: Given query is to find the equation of the tangent line.

Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: Suppose a product's revenue function is given by R(q) = - 8q² + 900q, where R(q) is in dollars and q…

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Q: Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find…

A: Given: rt = e-t, 5t2, 7 tan t To find: r't , r''t and r'(t)·r''t We know that  ddxex = ex ; ddxtanx…

Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

A: To find directional derivative of given function.

Q: Find the short test distinse between the two curves y² = Sinx"²" and x² + y² = 2 where intersect…

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Q: 5. Use Lagrange multipliers to find the extreme values of the f (x, y) = x² + 2y² subject to the…

A: By using Lagrange multipliers to find the extreme values of the function fx, y=x2+2y2 subject to the…

Q: 2x - 4 Find f ' (x) using the definition of the derivative: f ' (x) = lim h>0 f(x+h)-f(x) / h

A: Given query is to find the derivative using definition.

Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: Let's find least possible degree of given polynomial function.

Q: determine the limit lim x---> 0= sin (3x)/2x

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Q: d²y (2) Check that y = sint satisfies the differential equation dt2

A: We have to solve

Q: dt x(t) + 9 at dt 3x x(0)=8 x(0) = 9 x" (0)=12 then find x(0.25) a. (3 decimal P

A: we will find the required.

Q: You want to find the Fourier series for the funtion tan(x) over the interval -2π to 2π. Will the…

A: Follow the procedure given below.

Q: The function f(x) = 2 + 6x + 54x has one local minimum and one local maximum. This function has a…

A: The given function is: fx=2+6x+54x-1   First, we have to find the critical point by solving f'x=0.…

Q: Find ff f(x, y) dA where f(x, y) = 3x + 1 and R= [0, 3] x [1,3]. R SSR f(x, y) dA =

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Q: H.W: Salve the following equations.... 一乂 3. H .... Je A zAyf. (X² 3y)...........

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Q: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a…

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Q: (14) Give the appropriate form of the partial fraction decomposition. 2x+32 (x+1)(x+7)

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