Set up an integral that represents the arc length of the function g(x) = sin x for the interval [0, 37] in the form | f(x) da. a f(x) = a = and b

Q: Find the interval of convergence of the power series. (Be sure to lInclude a check for convergence a...

A: Here, the given series is: ∑n=0∞(-1)n+1(n+6) xn...(1) Let, an=(-1)n+1(n+6)xn, n≥1

Q: Find range of function f(x): b) f(x)= (2 – x)V 4x – x²,xE (0, 4) -

A: b)   f(x)=(2-x)4x-x2 , x∈(0,4)         plot the function on the graph    

Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then l...

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Q: Solve the differential equation with appropriate method. Express final answer equated to y^n. (e.g. ...

A: Given, The differential equation dydx-y=xy2 We have to solve the differential equation.  

Q: Solve the differential equation with appropriate method. Finalize answer free of fractions and equat...

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Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms and radi...

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Q: Falco Inc. financed the purchase of a machine with a loan at 3.07% compounded semi- annually. This l...

A: here is total payment after 10 year with interest = 8800*2*10 = $176000 now use compound interest fo...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: dx The integral can be rewritten as - 8. (a) lim (-2+ 2v1 ) (b) lim (-1+2v1 – s) | (c) lim (-2 + V1-...

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Q: Let x- sup(A) and if a E A, with x+ a, then which of the following statements is true? O There is E ...

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Q: dx For the integral f which of the following options is correct? A. lim -(x – 1)½ ", + lim (x – 1)/3...

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Q: Evaluate the integral dx ,2 2x x - 3x X

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Q: 3. A single-input, single-output system has the state variable representation *= Ax + Bu y = Cx 1 wh...

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Q: cSc x du 5. If u = f(x), then -. Compute f dx = sin x – cos x 2 (a) 1 (b) -1 (c) 0 (d) 2

A: ∫cscxsinx-cosxdx=∫duu

Q: Consider ſ* xe-**dx. What will be the appropriate solution and answer to this improper integral? lim...

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Q: Jared was receiving rental payments of $4,000 at the beginning of every month from the tenants of hi...

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Q: 9. Evaluate the integral ex V2e-2x – 3e2x 2/2e-2x – 3e2x +C А. 1 3eªx – 2+C B. 2/3 Arcan V3e2x Arcsi...

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Q: person’s approximate brain weight is directly proportional to his or her body weight, and a person w...

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Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =...

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the numbe...

Q: e3x 2. Let dx be given . If u = e* + 1, then the resulting integral is ex + 1 | f(u) du. Compute f(3...

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Q: Consider sequences On+(-1)". Which of the above sequences are monotonic: O A. (), ) and (). O B. ) o...

A: We have to find which sequence is monotonic.

Q: By inspection, find the following integral 1 dx 2(5 – 3x)

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Q: EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and...

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Q: Consider the function below. Is g continuous on (0,1]? on (1,4]? why or why not? if æ 4.

A: Explanation of the answer is as follows

Q: Learning Task 3: Find the equation of the tangent line to the following curves at a given point 1. y...

A: we need to find the tangent line of y=x2-6x+9 at x=2

Q: 4 り

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Q: Solve the following differential equations. Indicate the (Differential Equations) nethod/s used at t...

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Q: What is phase line

A: A phase line is a qualitative behaviour of autonomous differential equation in a single variable dy/...

Q: find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2, ...

A: To find the area of the region bounded above by the curve y=2e-x+x, below by the curve y=ex2 on the ...

Q: Use the difference an+1 – An to show that the sequence {n – 8"}=1 is strictly increasing or strictly...

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Q: dx reduces to du The integral 3. ex + 1 where u = f(x) and for some и constant k . Compute f(1). (a)...

A: Given

Q: 3 : - 5 7 Consider the sequences 1; - .Which of these statements is correct? :- - 8. 11 A. The seque...

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Q: Differentiate. You do not need to simplify.

A: g) given y = sinxexy' =dsinxexdxwe know that duvdx = vu'-uv'v2 

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their d...

A: As we know that the derivative of uv form is given by ddxuv=u'v-uv'v2 see below the answer and calcu...

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: Calculate the future value of the following ordinary simple annuities. Round the answers to the near...

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Q: 2 tan(4x-1)–3 cos²(4x-1) dy cos(4x-1) 4. If we let u = 4x -1 for the ', what's going to be the resul...

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Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

A: (4x2+y2)dxdy = -xy ....(1)f(x,y) dxdy =ϕ(x,y)The given differential equation is ahomogenous equation...

Q: Find the radius of convergence of the power series. (If you need to use es or -eo, enter INFINITY or...

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Q: Let a +0 such that (a+2) =0- Which of the following statements is correct? A. None of the choices in...

A: We want to find the correct answer.

Q: 1. It is the value for natural exponential fur 2.It is a function which is continuous at eve 3. It i...

A: We will solve 3 parts only 

Q: Matthew invested $875 at the end of every month in an investment fund that was earning interest at a...

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Q: finalize answer free of logarithms and radicals express. Express final answer equated to a constant ...

A: The given problem is solved below in detail.

Q: A 2005 study by the Fisheries Research Services in Aberdeen, Scotland, suggests that the average len...

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Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 6 6 2r – 6)* k...

A: Here we have to use sigma notation to write the Taylor series about x=x0 for the function f(x)=ex; x...

Q: Find the derivative of the following functions using the definition of the sine and cosine function....

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Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

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Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n>1              ..(i) We have to show that Sn  is not an...

Q: dx The integral can be rewritten as -∞ V1 – x (a) lim (-2+2vī1-s) (b) lim (-1+ 2v1 – s S--00 S--00 (...

A: Given ∫-∞0dx1-x Let t=1-x differentiating with respect to x, dt=-dx ∫-∞0dx1-x=-∫-∞0dtt=-∫-∞0(t)-1/2 ...

Q: Natalie wants to accumulate at least $40,000 by depositing $2,000 at the end of each month into a fu...

A: Given query is to find the the number of deposit to reach the goal and the time taken.