Find the limit lim x →∞ √1+ 2x + 9x² -2x + 5

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A: I am attaching image so that you understand each and every step.

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Q: DETAILS ZILLDIFFEQMODAP11 4.1.002. The given family of functions is the general solution of the…

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A: In this question, we want to verify the green's Theorem.

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: 5. Find (In 3) for a solution (y + x² e) dx - xdy = 0; y(ln 2) = 0 (x) to the initial value problem…

A: The given equation is; (y+x2ex)dx-xdy=0; y(ln 2)=0

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Q: 4. DETAILS ZILLDIFFEQMODAP11 7.R.004. Answer true or false. The function f(t) = (et) 10 is of…

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Q: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?.

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Q: Let vector A = and vector B = . Determine the vector projection of A onto B.

A: Topic:- vector algebra

Q: Find the derivative of the function f. 3 √√x If your answer has a radical, express it as a rational…

A: solution:-f(x)=3xf'(x)=ddx3x        =3ddxx-1/2        =3-12x-12-1        =-32x-32         =-32x32…

Q: The graph of f is shown. Apply Rolle's Theorem and find all values of c such that f '(c) = 0 at some…

A: The graph of f is shown. To apply Rolle's Theorem and to find all values of c such that f'c=0 at…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t)=…

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A: The solution is given below

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Q: Determine all critical points of the function f(x) = 2x(4- x)³.

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Q: 36-2 dzdx dy Rewrite the integral using the order dzdydx. (6x +36-1- 076 36-y 18 18 10 ² dzdydx dzdy…

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Q: Answer the following True or False: d Since dx d -sin (6x² + 3x + 4) = (12x + 3) cos x dx (6x² + 3x…

A: The objective of the question is checking the proper use of chain rule .

Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

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A: Please refer to the image below

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

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Q: Determine if the following series are convergent.

A: we have to check whether the series is convergent or divergent.

Q: 6. DETAILS ZILLDIFFEQMODAP11 4.5.045. Solve the given differential equation by undetermined…

A: To find out the solution of the differential equation by using the undetermined coefficients.

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.)…

A: O

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Q: ). Determine whether the series ∞ 2 cos(n?) n   n = 1 converges absolutely, converges…

A: answer is in next step.

Q: sin 2xdx 2+cosx

A: Our Aim is to evaluate the given indefinite integral using U-Substitution.∫sin (2x)2+cos (x)dx-(i)

Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 6tk ** kk Find its length over the…

A: Given problem:- rt=-ti+2tj+6tk , [0,1]

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Q: Consider the following. 4x -y + z = 6 Sketch a graph of the plane... O Y_6 X6 Y_6 X6 4 -4 4 2 N N 6…

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Q: If f(x)=√√1+y³ dy, find (ƒ˜¹)'(0).

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Q: Your answer is correct. Find a differential equation whose general solution is = = C₁e⁹t + c₂e-³t.

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