-4t Find the indefinite integral dt and verify the result by differentiation. (t2+3)3

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

Q: = - 1) ex²-x dx x. Use the substitution method to rewrite the function in the integrand, (18x – 1)…

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Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

A: Given ddx∫x5e7xlntdt.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given a function f(x) = 9x+14x2-sin(2x)   To Find: A linear operator that annihilates the given…

Q: 2. Evaluate the integral / sin'at dt

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Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: Solve the ODE by integration or by remembering a differentiation formula. 1. y+2 sin 2mx = 0 2. y+…

A: According to our company's guidelines I can only answer first three subparts of the questions since…

Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Find the indefinite integral and check the result by differentiation. dx 9x2 Part 1 of 7 Observe…

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Q: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Let D be the differential operator ddx, we have t find function f such that  fDgx=0, where…

Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Verify whether the function g(x) = 1- 2 sin x [1-(π/2)] is the solution of the integra

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Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The annihilator of a function is a differential operator which, when operated on it, obliterates it.…

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: (3x+4)2dx Evaluate indefinite anti-differentiation

A: The given integral is (3x+4)2.

Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

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Q: Use the Fundamental Theorem of Calculus to find the derivative of Cos t -dt t11 -3 dy dx II

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

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Q: Let y = f(x), where f(x) = (x-4)/(x^2+4).   Find the differential of the function.

A: Calculation: The first derivative of f(x) is given by

Q: Q8/ Use implicit differentiation to find of the following curve at the point (2, 3). dx2 2x3 – 3y2 =…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: H (w) s (+リ? (outて)

A: The given problem is to find the inverse Fourier transform of the given function, we have to split…

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: 2. Find the derivative of each of the following: (a) f(x)= 3" cos² (}x) %3D (b) h(x) = Vrd – 4x + 1…

A: (a) Consider the given function, fx=3xcos212x Here the objective is to find the derivative of the…

Q: 1. Use the "First Fundamental Theorem Of Calculus" to find the first derivative of the function. 2 –…

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Q: Find the differential of the function. 7 + uvw Da + | Dov•([ Daw dT =

A: Given function is By using quotient rule of differentiation

Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: Calculate the derivative d da 34 dt using Part 2 of the Fundamental Theorem of Calculus. 34 d dx…

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Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: Use the Fundamental Theorem of Calculus to find the derivative. Vx-x1-t2 dt d dx

A: The Fundamental Theorem of Calculus says: ddx∫ag(x)f(t) dt=f(g(x))·g'(x)...(1)

Q: Find the derivative of h(x) = cos (2x3 - 5). %3D Provide your answer below: W(x)= O %3D

A: We will find the derivative of h(x) in the following step.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus to determine…

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Q: Find the derivative. cos X d 78° dt dx 1 a. by evaluating the integral and differentiating the…

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Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. d dx re¹2x d dx x4…

A: This question can be solved using the concept of fundamental theorem of calculus part 2 according to…

Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x