Given f'(x) = -9 sin(3x) and f'(0) = 2 and f(0) = 5. ƒ(7) Find f =

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A: given  f(x)=8sinx d dx(sinx)=cosxstandard form of quation is y-y1=m(x-x1)where m is slope m=f'(x)

Q: 8. For which values of r does the following series converge? (-1)" η n=1 -(2x + 4)"

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Q: Question 3 Find the value of the derivative (if it exists) of f(x) = (x-2) 4/5 at the indicated…

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Q: 2. When a particle is located a distance x meter from the origin, a force of f(x) = 3x² + 4x…

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Find the derivative of the function. F(t) = e5tsin(2t) F'(t) =

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Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

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Q: 1. Use the differential form of the chain rule to find if y = ² and u = x² + 1. 2. Find the…

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Q: mine the average rate of change of f(x) = x³. - x over the interval 1 ≤x≤ 3.

A: We will find the required.

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Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c

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Q: Find f(g(x)) for f(x): = Of(g(x)): 6x² 18 Of(g(x)) = 17x² + 1 O f(g(x)) O f(g(x)) O f(g(x)) = 6 17 +…

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Q: 14. The domain of the function is y 4 2 -4-20 2 4 x

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Q: Find √ √1 + x²dx

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Q: Verify that the given differential equation is exact, then solve it. 10x 24y 16y 5x (3) dx + X y 4 X…

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Q: 4. Consider the graph to the right, containing the points (0, 1) and (1, 5). A. What function is…

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Q: . In the Gizmo, select sine wave so the parent function is f(x) = sin (x). A. The sine wave is a…

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Q: 4. Find the length of the logarithmic spiral r = e ¹2 from 0=0 to 0=2

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Q: Find the linear approximation to the equation f(x, y) = 3₁1/ approximate f(4.14, 2.19) xy at the…

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Q: The graph of y = f(x) has ƒ(5) = -2, f'(5) = 2, and f'(5): = -1. Which of the = −1 following might…

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Q: ← Give integers p and q such that Nul A is a subspace of RP and Col A is a subspace of Rª. A = 1 245…

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Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

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Q: Implicit Solution (2xe ³4+ex) dx + 13x²e ³4 - y²) dy=0

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Q: a = (0, 1, 2), 128. c= (1, 0, 1) - b = (-1,

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A: Consider the function f(θ)= 7sin2θ-7cosθ.  a) Find f' b) Find the critical points on the interval…

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Q: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…

A: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…

Q: Question 18 Show that the equation has exactly one real solution. 207e+2023 In x = 7724

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Q: Find the derivative of the function. y' = -1(x - √ ₁ + x²) 1 y = 9 tan-¹(x-

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Q: The functions describes the distances from the origin at time t of an object in rectilinear motion.…

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