For the equation given below, evaluate y at the point y - 6x² + 24 = 0.

Q: 1 Defennire it the following series is Convergent divergent. E n=1 3 ²+2

A: since multiple questions are asked, I am answering first question

Q: Find the solution of the given initial value problem in explicit form. 114 y(x) = y' = (1 – 3x)y²,…

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Q: Find fxx fxy, fyx and fyy, for the following function. (Remember, fx means to differentiate with…

A: The objective of the question is determine the second order partial derivative.

Q: (jw+4) (jw+3) (jw+2) B + (jw+3) (jw+2) A(jw+2)+B(jw+3) (jw+3) (jw+2) Ajw+2A+Bjw+3B (jw+3) (jw+2)…

A: We will use properties of partial fraction

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Q: Suppose that f(x) = J'(-2) = f(1) = 6x + 16 x Evaluate each of the following:

A: Recall: Quotient rule y'=vu'-uv'v2 We have, u=6x+16, v=x

Q: 1. Given r(t) = <In(cost), -1, 2 $₁ 2 A a) Find the length of the curve for r(t) at 0<t< R|4 b) Find…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Evaluate the limit using the Basic Limit Laws and the limits limx→ex/q = cpla and limx→ck = k. (Use…

A: The given problem is solved below in detail.

Q: If a differentiable function f is decreasing on (a,b), then f'(x) < 0 for each x in (a,b). A) True B…

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Q: Tim x-2 x-2 Js √5x-2-√√2x+4

A: To evaluate the given limit first we multiply the numerator and denominator by the conjugate of the…

Q: 4. Let f: [a, b] → R,g: [a, b] → R, and x E [a, b] such that f'(x) and g'(x) exist, g'(x) = 0, f(t)…

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Q: Evaluate the integral. Oin | +0 | C In (x-8)² x + 7 In |(x-8) ³² (x + 7) + Din ((x=83² ) +1 In C + 7…

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Q: Find F as a function of x and evaluate it at x = 2, x = 4 and x = 7. F(x) = F(2) F(4) = F(7) = F(x)…

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Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy

Q: A particle moves along a straight path with velocity of v(t) = (4-4t) m/s at time t seconds. What is…

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Q: your final answer at least three (3)decimal places.   Find the area of the region under the curve…

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Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A: Here we have to choose the correct option.

Q: Let f(x) = 4x6 In x f'(x) = Rounding to 3 decimal places, ƒ' (e²) =

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 7" 57n3 Σ(-1)-1_ n =…

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Q: Solve the given differential equation. 11x² – 1 11 + 5y y' =

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Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

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Q: A pilot is flying from Daytona Beach to Prescott. The two cities are 1874 miles away from one…

A: Let speed of light  = Va         wind speed  = Vw = 12mph  let flight flying direction WαN       ⇒…

Q: Find the equation of the plane that passes through the point (4,-1,2) and is orthogonal to the line…

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Q: Find the slope of the tangent line to f(x) = √9x³ at the point x = 4.

A: We have to find the slope of the tangent line to f(x)=9x3 at the point x=4.

Q: se the if f₁(t) properties of Fourier transform ē at ult) = (w) = JF.T -=S² f(t) ējwt dt -0 -jut =…

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Q: dz 2 ē j ( W ± ¹ ) ( x (Z) e ³ (W+¹) Z dz 2 BO t AN Z 2dt = dz t = How did he get the value inside…

A: Multiply the term in power of exponential and then use am+n  = am * an Since, one term is constant…

Q: f(x) = 2x + 5

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Q: 12. Consider the differential equation: 2a + (b₂+ a(a +1) df dz Z d² f dz² + a(a + 1) √(z) = 0₁ Z a,…

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Q: 7-8e2x lim x→→∞ 12e²x+28

A: To find the limit.

Q: 6° x³ (x² + 8)² converges diverges dx Evaluate the integral if it converges. (If the quantity…

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Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: #2. Find the sum of the 8 n=1 1 (3n+ 1)(3n+4)

A: In given series we break the nth term of series as addition of nth term of two different series…

Q: Given y(4) - 6y" - 36y" +216y' = t² +8+ t sint, determine a suitable form for Y(t) if the method of…

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: I need a box with a square base and an open top that can hold 500 in What is the least amount of…

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Q: A rectangular area adjacent to a river is fenced in; no fence is needed on the river side. The…

A: To find out the dimensions.

Q: Use the properties of Fourier transform if f₁(t) = ē at ult) JF.T = S flt) ējwt dt ماز- Seat, ejust…

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Q: Find the surface area of a cylinder with a base radius of 2 in and a height of 6 in. Write your…

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) z√z…

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Q: jw)² +5jw+6 =(jw)² +3jw+2jw +6 =jw(jw + 3) + 2(jw+3) (jw+3)(jw+2)

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Q: y' =+y(y+2), y(0) = - 1

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Q: 2. Find the curvature of f(x)= x cos²x at x = π

A: The solution is given below

Q: I need help understanding this particular question.  I will be tested on ones like this so if I…

A: Topic:- application of integration

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: Consider the following series. n= 1 (a) Use the sum of the first 10 terms to estimate the sum of the…

A: Given an =1/n^5

Q: Find the slope of the line tangent to the graph of f(x) = -x-1 at x = -3. Provide your answer below:…

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Q: Test the series for convergence or divergence. 8 Σ· n = 1 2 n

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Q: lim X→ x A B C D √√x³+3x²+7 4x²+3x+4 0 ∞ 1 4 11 = Some other answer

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