1. If f(r) = 3 find f(x) I – 4' |

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

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Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: find the antiderivative F(x) of f(x)=x^2+sin(x)+3 with F(0=8

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: If; of t = x then at t=1 is (Note that these functions in N) dx

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Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

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Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

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Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: f(t) = t sinh 5t 5s 5s А. (s2-25)2 С. (s2 +25)2 10s 10s В. (s2-25)2 D. (s2 +25)2

A: We find the Laplace transform of  f(t)=tsinh(5t)

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: Q.4 Find the most general antiderivative of the function 1) f(x) = 2x + 1 2) f(x) = cos2x + sin3x…

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Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: y' + 4y = e^(4t) %3D

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Q: If µ(x) ef (x) is an integrating factor of linear D. E x y' + xf(x) y = x* y – x² sin x where f' (1)…

A: To find - If μx = efx is an integrating factor of linear D.E. x3y' + xfx y = x4y - x2 sinx, where…

Q: 1) In this problem, let * = 2, the value Ar = dx, dy = f ' (x)dx, and Ay = f(x + Ax) - f(x) to…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: d ** If g(x) = [e² – In(2t + 1)]at , find g" (x) dx A ex- In(2x + 1) 4 ex - (2x + 1)2 B (c) none of…

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Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: Find the general antiderivative of f (x) = 4 x ln x²

A: Given: fx=4xlnx2

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: 3. Express the general solution in terms of Bessel functions: z²y" + 4ry' + (x² + 2)y = 0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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Q: 5. What is the most general antiderivative of the function S(2) = z - 2, in other words, what is -…

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.