Could you help me with this? Determine the area between the following functions (do not forget to put the steps)

Q: -+inf In(tan¯1x) 1+x2 1

A: ∫1∞ln(arctan(x)1+x2dxSubstiute u=arctan(x)→dudx=11+x2→dx=(x2+1)du=∫ln(u)duIntegrate by parts…

Q: n(x – 2)" 3" (2n – 1)3 - Consider the power series n=1 a. Show that the power series converges when…

A: We have to check the given series is convergent for x=5

Q: Shetch the region in the plane consisting of points whose polar coordinates satsfy the given…

A: Shaded area is the required area

Q: Solve the following equation: 16ª = 8ª+1 O 3 O-3 O 1

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Q: 1 dx cos² 2x 3. 4. x² sin (x³) dx S elnvx+1 dx 5.

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Q: Write the partial fraction decomposition of the rational expression. Check your result…

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Q: Determine whether the following series is convergent or divergent (-1)"3n² 4n2 –1 (b) n=1

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Q: Determine whether the series is convergent or divergent. (-1)"3"² En=1 2 -1

A: An absolutely convergent series is convergent. P-Test: The series ∑n=1∞1np converges if p>1 and…

Q: 2.x3 – x² + 2x – 2 dx x² (x² – 2x + 2) -

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Q: Determine the third degree Maclaurin polynomial of f(x) = tan 3x. Use this to approximate the…

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Q: A model created by an engineer is represented by the following multivariable functions w = xe%, x…

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Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: m m 2m + 1. m=1 т m 2m + 1 m=1 Do the following converge or diverge?

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Q: 570 8. The demand function of an electronics company's car stereo is p(x) Find the 2х +7 consumer…

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Q: 2. Use integration by parts to evaluate the following. (a) Sx tan- x dx

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Q: given series is convergent 2"

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Q: LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 1. (9Dª + 6D³ + D²)y = 0 2. (4Dª – 45D² – 70D – 24)y = 0

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Q: Find Duf at P. 1 1 f (x, y) = 5(4+ xy)3/2; P(3,4); i+ j и %3 V2 NOTE: Enter the exact answer. Duf =

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Q: | #(9 – In² x)5/2 dx I. Evaluate the following integrals. 1 1. -d.x x(9 – In? x)5/2

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Q: 4x + 1 dx Jx3 + 3x2 - 6х -36 2.

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Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or divergent { an } n=1

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Q: x² dx J (² – 25)5/2

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Q: In Sx-/25+> 25+ x2 dx , we let x = 5sine. (A True B False

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Q: Integral

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Q: V9 – 4x2 Evaluate: A f (x) = V9 – 4x2 + 2 sin () + C V9 – 4x2 – 2x sin- () + C B 6/ | | f (x) = f…

A: For the solution follow the next step.

Q: Solve the D.E dy + (xy – xy²)dx = 0 %3D

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Q: Consider the following. f(x) = x4 + 6x² – 27 (a) Write the polynomial as the product of factors that…

A: The given polynomial is f(x)=x4+6x2-27 ........................................ (1)

Q: х2 — х — 2 lim х-2 х2 + х — 6 1. О 1 2. О 4/5 3. О 3/5 4. О 2/5

A: To evaluate: limx→2 x2-x-2x2+x-6 First factorize the numerator and denominator

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: ralue of (2) for z= 2.36. (note: use 2 decimal places)

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Q: d -sin 6 if0 is given as dx What modifications would have to be made to find the derivative an angle…

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Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: n Vy(x- y) + y² + 6

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Q: Sllerch the graph of the 18r=4sine given polacequations

A: Given

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: 1. Y = 2 – 7.x fa) — 4 — 5х — 21? 2. 3. Y = 2x³ – 3.x

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Q: Write the integral that would be used to find the volume of the solid generated when the region…

A: Given line 2x+y=6, That is y=-2x+6. x -intercept of line 3 y - intercept of line is 6 We know that…

Q: y= ( х-6 3 1. у %3 Зx+4,

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Determine whether the following series is convergent or divergent 3- Vn (a) 2 n=1

A: The given series is: ∑n=1∞3-n4n34,an=3-n4n34, n≥1f(x)=3-n4n34

Q: Using the squeeze theorem, find the value of lim,0 x² sin=) O 1 O -1 O does not exist

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Q: 1 In solving the antiderivative of f(x) = 2- 3sin(x) by miscellaneous substitution, the substitution…

A: Given: fx=12-3sinx To find: ∫f(x)dx We know that, sinx = 2tanx21+tan2x2

Q: 5. y = Arctan²(x³) 6. y = Arccos (

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Q: 3. 2+ 1+ +++ ++ + 2m -2m

A: Answer : y=5sin(x/3)

Q: 2.x3 – x² + 2x – 2 dx x² (x² – 2x + 2) - -

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Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: 5- 4- Find the volume of the solid created by rotating the following curve y = 3vx about the y-axis.…

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Q: (2.) (1-(In))^ (3.) yn + sin ()

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Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: If substitution technique is used to solve the integral [(12.x+3x* )(10x² +x³ – 2)° dx then the…

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