15 Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Center (-1, 1/3) (-2/3, 1/3) (-8/9, 1/3)

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We have to integrate the given function for the given limits

Q: π/2 sin (cos() sin() dx (Consider initially the first 2 terms)

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Q: Consider using the method of partial fractions to solve x²+x+1 rb Sa 2x²+2+x²+x - dx = [Af(x) – B…

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Q: Please solve the problem with complete solution. Thank you

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Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: (C) EXERCISES Evaluate the following integrals: 1. tan² x dx 2. cot cot² r dr COS I da sin x COST…

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Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-

Q: Find dy/dx

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Q: 23. ["Se' dx 5e* 2 24. S/2 ze de dx 2x

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Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: 15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can…

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Q: II. Find Do not simplify your answers. da 1. log, (√2x² + y) + tan(x² − ³) = sin¯¹ (2² − 1) + 2

A: log3(2x23+y )+tan(xπ-πy)= sin-1(x2-1)+π21log(3). 2x23+y 23×23x-13+y'+sec2(xπ-πy).(πxπ-1-πy.…

Q: 8 An acceleration function is expressed as a (s, v) = s²- determine displacement by integrating '…

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Q: Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. f(x)=…

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Q: dy II. Find Do not simplify your answers. da 1. log3 (√2x² + y) + tan(x - 7") = sin ¹1 (x²-1) +

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Q: 27 If (2x 3) [133] [3] 3] -3 23 1. 2 13 2 2 3. 13 2 23 2 - 0, then the value of x is

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Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: Question 4 Solve the equation: 1²+t+19-0. Fully simplify all answers, including non-real solutions

A: The given equation is: t2+t+19=0

Q: d²y 2 dx² dy dx 6y=e²x

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Q: ♫/² sin ( cos() sin (²) dx (Consider initially the first 2 terms)

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Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ....…

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Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: Integrate the following functions f(x,y) = 3x-2y. R: over the given regions. the circle x² + y²

A: Given function f(x,y)=3x-2y and region R is x2+y2=1

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: x²+x+1 Sa 2x²+2+x³+x² (A (B (D) -b dx dx = [Aƒ (x) – B ln(g(x)]å + D ſb da , and if A = ‚B < 0, then…

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Q: sec+2x tan 2x and -dx 11 1 I + 12 tan 2x 16 tan³2x Ⓡ (cor³2x) ( 1+3csc22x 12 Ⓒ/cot²2xcot³21+C 16…

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Q: of

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Q: 20 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Write 20 terms of the Fibonacci sequence

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Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given: r(t)=t i+6ti

Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

Q: Select the conic section represented by the equation. x 2 +y 2 + 6x - 4y - 12 = 0. circle point…

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Q: Evaluate 5 (²) 4. dy -2

A: ∫-2-1 (y-2)dy/y ∫-2-1 (y - 2/y)dy [ 2y3/2/3 - 4y]-2-1 -2i/3 - 4i +42i +42i -14i/3 +82i

Q: 62. du * |x|dx

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Q: II. Find 2. y = Do not simplify your answers. dx tan ¹(cosha) (sin² x)(secha)secz [use logarithmic…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ 7x + 3xy² dx…

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Q: 7. Do as indicated. 1 1. Let f(x)= = Find the equation of the tangent line to the graph of f'(x) at…

A: This question is related to straight lines, we will solve it using given information.

Q: For each of the following integrations, choose the method that can be used to find its solution.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 7. lim y→∞ y² – е6 y 4y² + e7y

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Q: which of the following sequences is converge or diverge: (²√m) ()}. {!}

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Q: if it was a bez Prove that لما لها حاطها

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Q: Solve the given differential equation. All solutions should be found. dy_x³_8y x5 - 8y dx X NOTE:…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim x-3 (x-3) tan(9-x²)…

A: As L'Hospital's rule is not to use so I have used the expansion of sin and tan function and easily…

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Let (A) = and B = . Find the angle between BO and A D O 【cos) 2/√(30(21)) O [cos] ^(-1) 2/√(30(21))…

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Q: y"+6y' +8y=10e-³x ;

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x- (x² + x)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to identify the quadratic surface.