Find the derivative of G(x) = √ x³ t.csct dt. O-3x5 csc r³ cot x³ -3x² csc x³ cot x³ Ox³ csc x³ O-3x5 csc x³ O-x³ csc x³

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s. f(t) = et cosh(t) L{f(t)}…

A: Note: Since the student has not given Theorem 7.1.1 to find the Laplace transform, so we solving…

Q: ) . Is the differential equation linear? dy dt + y4 = x

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Q: Consider the following function. f(x) = x + (-4,-5) (a) Find an equation of the tangent line to the…

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Q: Find f'(x) and f'(c). f'(x) f'(c) || = Function f(x) = x cos(x) √3-1 2√3 3-√3 6 or Value of c C =…

A: Given  fx = x cosx  and  c=π3. We have to find f'x and f'c.

Q: Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). What is the period of the…

A: Let's draw the graph of trigonometric function.

Q: Is it possible for a function f to attain only positive values (that is, f(x) > 0 for all x) and…

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Q: A tank initially holds 50 gal of a brine solution containing 2 Ib of salt. At t = 0 another brine…

A: Given data:- Volume of brine solution, Vo=50 gal Containing salt, a=2 At t=0 any Brine solution…

Q: x+1, x < 4 Let f(x) = x-4, x ≥4 Explain why f is (or is not) continuous at x = 4. Explain why f is…

A: Topic:- calculus

Q: 3. A wheel has a diameter of 70 cm and completes a revolution in 0.25 seconds at top speed. a.…

A: Angular velocity= θ/t , θ= 2π×number of revolution per unit time  Linear velocity= radius× angular…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Evaluate the integral using the following values. 8 ["x³ dx = 960, ["x dx = 24, ["dx-4 = J4 8 [²- x…

A: Gievn , Hint: 4∫8xdx=24   .....(1)

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}:…

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Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: ENAS X dx 1+419x

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Q: Solve: y(1) Given: y" + y = k sin(kt), y(0)=6, y'(0) = 0, where k-sqrt(2)

A: y" + y = k sin(kt), y(0) = 6 y'(0) = 0, where k = sqrt(2)

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Describe the x-values at which is differentiable. f (x) = { 3²-7 x²-3x≤0 3-x²x>0 T -2 2 -2 The…

A: Let's find function is differential or not.

Q: Sandy's main house is a hemispherical glass dome with diameter of 8m. Suppose that the glass is m…

A: NOTE: Refresh your page if you can't see any equations. . the diameter of the hemisphere is 8 m so…

Q: 4x A. dx - 3 4 4x A=²³cof=1¹³) + C__ _B. — co(=^^) + C +C 4 4x c. ²2 cof=14) + C 4x D.= co(-1) +

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Q: Graph to the image below and find the volume of the area bounded by y = (x^2 - 4)^2 and the x-axis,…

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Q: Consider the following graph: 28 14 1 3/14 6,28 x a) Write an equation for the graph with a single…

A: Given

Q: Find the standard form of the equation of the ellipse and give the location of its foci

A: Here we have to find the equation of an ellipse.

Q: Suppose the Maclaurin series of a function is f(x)=2+3x+2x² + x³ + x² + .. Find the first four…

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Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: II YOLUMES OF REVOLUTION 1. Find the volume generated by revolving about x-1, the area bounded by y…

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Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

Q: solve by hand( numerically) f(x)= cos(x)-x exp (x) using the bisection method and Newton- Raphson…

A: Let f(x)=cos(x)-x exp(x). Here f(0)=1&gt;0 and f(1)=-2.178&lt;0 Now, Root lies between 0 and 1.…

Q: x4 x² x² + 1 - 1 dx ii) Š 1+ Inx

A: Please refer to the image below

Q: The graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation…

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Q: # (u²-1)4 (u² + 1)4 du

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Q: ydx+(x-y)dy=0

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. A = 4 y = x² + 4 y = x x

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

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Q: A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the…

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Q: (x-4) dx 2 x²+x-6

A: We can evaluate the given integral by using the partial fraction method.

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: We have to find  the volume of the solid that results when the shaded region is revolved about the…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: So sin¹ (6x) cos (3x) dx

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: Find the sum of the first 6 terms of the following sequence. Round to the nearest hundredth if…

A: Our Aim is to find the sum of the first 6 terms of the following sequence givenbelow:-8, 4,…

Q: Consider the Gompertz equation, a modification for logistic growth, which is often used for modeling…

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Q: 95. Solve each system of equations. a) 2x - 4y + 5z = −4 3x +2y-z = 1 4x + 3y - 3x = -1 b) 5x + 4y +…

A: To solve each sytem of equations.a 2x-4y+5z=-43x+2y-z=14x+3y-3z=-1b 5x+4y+2z=73x+y-3z=27x+7y+7z=12

Q: Graph the integrand and use areas to evaluate the integral. 5 S (5-1x) dx -5 A. 50 B. 75 C. 25 - 2…

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Q: f(x) = 2 x-6x-7 8-2

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) g(t) =…

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Q: what theorem was used? i cant read it.

A: Let's solve.

Q: Evaluate the following integral: 2x 3xy SS²*13 (2y)dzdydx x

A: A detailed solution is given below       We know that ∫xn dx =  xn+1n+1

Q: If the work required to stretch a spring 2 ft beyond its natural length is 12 ft-lb, how much work…

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Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Let, each square as one unit. Graph :

Q: S: z = √x² + y², (x-1)² + y² ≤ 1

A: