3) Convert the following polar equations to rectangular equations. 1 a) r = b. r=4 4 cos 0-3 sin 0

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A: Please find the solution

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A:

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A: Here, the given series is: ∑n=12∞n+5n! Let, an=n+5n!; n≥12

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A:

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A: Let's find.

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A:

Q: 4) Determinė the equation of the tangent to f(x) = -x² + 3x+1 that is perpendicular to the line x+2.…

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A: Given query is to find the value of indicated derivative.

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A:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

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A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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A:

Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

A: Solving

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A:

Q: Ql Find Ax

A:

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A: The given integration,         ∫x dxx-1

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A: First we sketch the region of integration then change the order of integration.

Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

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A:

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A:

Q: ey -2Vy-5inlVy+5| +C Vy+5 A) True False

A: I = ∫dyy+5 Let, y = t2   ...(1) Differentiating both sides, gives dy = 2tdt  ...(2)

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A: Given:      y = x3       y = 4x

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A:

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A: follow next step

Q: UsinG PYTHAGORE AN IDENTITY, SOLVE FOR [sin Gx) - cos (Vx)] - 3x5 COS

A: The integration of the integral is  [sinx1/3-cosx1/3]2/(3x2/3).

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A: NOTE:- AS PER BARTLEBY GUIDELINES, WE WILL ANSWER ONLY FIRST THREE PART OF THE QUESTIONS.

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A:

Q: The general solution of the second-order linear homogeneous differential equation y" +6 y=0 is y=…

A: Let's find.

Q: = sin? (esint) l(x) = tanh-1 x + In v1- x2 2 h(t) + cos + cos¯ -1(2t3 - 5) |

A:

Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: 20 Q41. Term independent of x in expansion of is? бх3

A:

Q: Find:  ∫5-9x/ (x-1)(3x-2) dx  where x > 1.

A:

Q: In XVX2-625 dx , if we let x-25sece, then dx = 25secede. A True B) False

A:

Q: If f(x) is odd and ∫−1 5 f(x)dx=14, then ∫1 5 f(x)dx=

A:

Q: S sec°x tan x dx +C + C sec³x + C

A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

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A:

Q: n(-8)" Use the ratio test to determine whether converges or diverges. п! n=25 (a) Find the ratio of…

A: Here we have to use the ratio test.

Q: S tan³ 6x sec10 6x dx 1 sec1²6x + sec1º6x + C 72 1 60 B none of the choices 1 -sec1²6x + 72 1 1…

A:

Q: Find the values of a and b for the curve x*y+ay =b if the point (1,1) is on its graph and the…

A: Given,            The curve is x2y+ay2=b if the point 1,1 is on its graph and the tangent line…

Q: Reduction of order can be used with yı = 2x to find a second solution for the %3D DE: 2x²y" – xy' -…

A:

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: Prove the identity. x2 - 1 tanh(In(x)) %3D x + 1 tanh(In(x)) %3D cosh(In(x)) eln(x) 2 -In(x) + e -1…

A:

Q: Question 8 = 1 and lim,→a g(x) |8(x) If limx→a ƒ(X) = 0 then, we must have limx→a [f»]«® = 1 True…

A: We are authorized to answer one question at a time ,since you have not mentioned which question you…

Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: a. f(x) = 4x + 11 find:f'(-2) %3D b. f(x) = 2x2 - 5x – 3 find: f'(2) %3D

A: derivative

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: Question 8 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. (A True…

A: We can evaluate the given integral by using the substitution u = csc (5x)

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A:

Q: Given (x + 4)(x – 2) f(x) = x2 —2(х — 8) - f'(x) = x3 4(х — 12) f"(x): - x4 (a) Find the domain of…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…