Determine the arc length parameterization of the circle x^2+y^2 =a^2 with orientation counterclockwise and (a, 0) as the point of reference

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Q: 5. у %3D 88 8x + 888 6. у %3D 2021 7х'6 7. у %3D 5x3 е 4x -5 8. у %3D 20 е -4x x2 - 10

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Q: The number of tree species S in a given area A in a forest reserve has been modeled by the power fun...

A: S(A)=0.882A0.842S'(A)=0.882×0.842×A0.842-1 S'(A)  =0.743A-0.158

Q: 1+ In x 6. Find f(x) so that when u = f(x) the integral J tan(f(x)) dx can be rewritten as | cot u d...

A: This can be evaluated as follows:

Q: One of the following is an improper integral. - In 3 e* dx 4 – ex dx In 2 xV16 – In x dx cln 2 dx x ...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)4 = f(x) = D %3...

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Q: y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0 solve using integrable combinations

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Q: Q10

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Q: Is the series divergent or convergent? With solution and explanation. +oo El-1)» (2n)! 2n n=1

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Q: Determine the set of values of the continuous function defined by the formula: a) f(x)=cos sin

A: Given that fx=cosπ3sinxgx=π3sinxsinx is continuous in x∈-∞,∞gx is also continuous .Range of sinx is ...

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

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Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

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 nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 3 P (X) –

A: Taylor polynomial of 4th order of function fx at a is defined as: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x...

Q: %3D (e) The characteristics of uz + Uyy = 0 are given by: dy (A) dx dy =-1 and (B) dx %3D = -1 dx dy...

A: Given:uxx+uyy=0

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: Find the radius of convergence of the power series. 00 E(-1)"n+ 9 n = 0

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Q: 2. Solve example 2 of rational inequality. You can refer to example 1 for the gide steps Example 1 3...

A: Inequality

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

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Q: Use sigma notation to write the Taylor series about x = xo for the functi e*; xo = 6 k=0 e6 k! k=0 k...

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Q: u du Form Answer Ex. S 3+ 2cosx 5sinx 5 -5V3+ 2cosx + C dx 3+ 2cosx -2sinxdx ī du 3 15. Given: S -dx...

A: This is a integration problem

Q: f(x) = x'- 12x + 2 3

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Q: Given the taylor series for ex= 1+x+1/2!x2+1/3!x3+...+1/n!xn Find the taylor series at 0 for e2x^...

A: taylor series for e2x2 at x=0

Q: (a) The eigenfunctions of the following eigenvalue problem: X" + XX = 0, X'(0) = X'(#) = 0 %3D are g...

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Q: Calculate the amount of money Kayla had to deposit in an investment fund growing at an interest rate...

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Q: 3. Show that the Maclaurin series for f(x) = (1+x)*, where k is any real number, is (1+ x)* = E k(k ...

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Q: A contract requires lease payments of $800 at the beginning of every month for 6 years. a. What is t...

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Q: 6. Find f(x) so that when w fG) the integral 1+ Inx dx can be tan(f) cot u du. rewritten as (a) x+ 1...

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Q: 6. Suppose a bakeshop purchased an equipment worth P 100,000 equipment, which was expected to last f...

A: Cost of the asset = 100,000 Salvage Value = 8,000 The useful life of the asset = 5 years Depreciati...

Q: Set up an integral that represents the arc length of the function g(x) = sin x for the interval [0, ...

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Q: e) Explain how one can use differentiation to analytically determine the slope of a curve

A: If cost revenue given , we differentiate it so we give marginal revenue. 

Q: 5. Complete the following short answer questions.. You do not need to show any work. 3 a. Express th...

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Q: 7. Determine f (x) so that cos(In'x) f(x) dx = sin(In'x) + C %3D (a) 2 In x 2 In x (b) (d)

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Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

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

A: Given :∫dxex+1

Q: x3 + 3x2 + 4r +1 dx (r2 + 2x + 2)2

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)4 Σ f(x) = n = ...

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Q: Is the series divergent or convergent? With complete solution and explanation +o0 (-1)" n! n=1

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Q: Evaluate the integral cot 2x S- Vcot2 2x – 15 V cot? 2x

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Q: Assume that the domain of f is the set A = {–5, –2, 0, 2, 3}. Determine the set of ordered pairs tha...

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Q: If a <b <e_ If lim a,=L and lim e,=L+7,then which of these is TRUE? - 00 - 00 O A. (b,) converges. O...

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

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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: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 7 P4(x) Nee...

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Q: Calculate the derivative indicated. d'y where dx? Ix=8 y = 6- x3 + 5x?

A: We need to calculate the second derivative of : y=6x3+5x2      at x=8

Q: 1. F- x/x is a weekday) Roster Method 2. G- (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) Verbal description metho...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) %3D (1 + x)5 f(x) =

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Q: e) y= cos(s" ) f) y= 2sin x

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

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