+∞ Σ η=1 η n' + 1

Q: Find any local and absolute extrema of the function f(x) = ². 9

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Q: solve the inequality algebraically 2x / x -3 > 3x / 2x+4

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Q: Suppose that for a given curve defined parametrically, dy dx dt = sint. Then dx² dy dt = tant and

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Q: Question 6 3 (1+x²) y' = 2xy(y³ - 1)

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Q: Question Determine the sum of the convergent series below. Leave your answer as a fraction in terms…

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Q: Calculus Find the standard deviation of the scores: 5.5.5. 8. 11. 11. 11. Round to tenths A) 2.8 B)…

A: To find the standard deviations

Q: A particle moves along a horizontal line so that its position s at time t> 0 is given by: s (t) =…

A: Given query is to find the velocity of the object.

Q: Define Q as the region bounded by the functions f(x) = and g(x) = 2x in the first quadrant between y…

A: Find the volume of the region bounded by f(x)=x24and g(x)=2x in the first quadrant between y=2 and…

Q: Example 2: Find the area of the region enclosed by the curves y = 2x - x² and y = x³ that lies in…

A: We have to find the area of the region enclosed by the curves y = 2x - x2 and y= x3 that lies in the…

Q: Consider the following. 3x³ - 27x² + 5 y = (a) Find the critical values of the function. (Enter your…

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Q: Let A be a square matrix such that det A = 5. Let B be the matrix obtained from A by multiplying the…

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Q: Given: y' +=(1-2x)y4 and y(0) = 1, Find C 3 3 OA. O OB. 1 OC. 2 OD. 1/2 OE. None

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Q: icle moves along a horizontal line so that its positions at time t > 0 is given by: = 2t³ - 18t² +…

A: Topic:- application of derivatives

Q: Solve 6 cos(2/3) = 6 sin² (3) + 4 for all solutions 0 < 3 < 2π B = Give your answers accurate to at…

A: Given 6cos2β=6sin2β+4 and 0≤β≤2π

Q: Suppose that f(x, y) = r²- xy + y² - 2x + 2y with D= {(x, y) | 0≤x≤2,0 ≤ y ≤ 2}. 1. The critical…

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Q: I dont understand what is written. Can you write in another way or atleast have spaces in between…

A: Here we have to determine the sum of convergent series.

Q: Consider the DE x³y' + 8x²yy' + 4xy²y³ = 0. Making the substitution v = y/x in the DE yields 1 + 8v…

A: We need to write that the equation obtained after substitution is true or false.

Q: Sketch the graphs of the following functions. 9. f(x)=x³-6x² + 12x-6 10. f(x) = -x³ 12. f(x)= x³ +…

A: Sketch the graphs of the some given function. 9) f(x)= x3 -6x2 +12x-6 11) f(x)= x3+3x+1 13) f(x)=…

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: The extreme value problem with both a maximum and a minimum value.Use Lagrange multiplier to find…

Q: d Calculate the derivative (r x r'), where r = (5t, t²,e¹). dt (Give your answer using component…

A: Find the derivative of cross product of vector r and its derivative.

Q: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2). (Enter your…

A:

Q: 3. Find the largest domain (in R2) for the function In(y-1) √x f(x, y): =

A: The given function fx,y=lny-1x We have to find the domain of fx,y

Q: 4) Show that the surfaces 3X² + 2Y²+Z² = 9 and x² + y² + Z²-8X-6Y-8Z + 24 = 0 have a common tangent…

A: We have to prove both surfaces have common tangent at P(1,1,2).

Q: Determine the type of DE (select all that applies): 2xy dx + (y² + x²) dy=0 Linear Exact Separable…

A:

Q: Find an equation for the tangent to the curve at the given point. Then sketch the curve and the…

A: The given function y=-2x3 at the point 1,-2 We have to find the equation of the tangent line and…

Q: Find the vertical and horizontal asymptotes. (Enter your answers as comma-separated lists of equatio…

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Q: Let f(x) = f'(x) = = 4 cos x + 5 tan a ƒ' ( − 7 ) = = Question Help Video Morrago instructor (round…

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Q: x + 3 x²-x-12 a) Determine the following key features of the function: i) domain and range Consider…

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Q: 29. Parametrize the part of the intersection of the surfaces y²-2² = x - 2, y² + z² = 9 where z≥ 0…

A: Given equations:- y2-z2=x-2 y2+z2=9

Q: Find the equation of the tangent line to the function f(x)=−3x3−3x2−x+3 at the point (−1,4). Give…

A: See this solution in below.

Q: Given that; f(2)=2, f'(2)=3 g(2)=6, g'(2)=4 Calculate the following (fg)/2= (f/g)'(2)= (g/f)'(2)=

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Q: Find the equation of the tangent line to the curve x² + y² + 2x + 1 = xy-8y at the point (-1,-9).

A: Given equation of the curve is  x²+y²+2x+1 = xy-8y We have to find the equation of tangent So slope…

Q: Find the general solution of the equation y'' + 5y' - 6y = 0 Use lower case c₁ and c₂ for the…

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Q: Determine the required integrating factor: y dx + (2x+1-xy) dy=0 O x²e-x y²e-y xe ye -X

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Q: can be written in the form. -8 ƒ (x) = -a(x+b)(x+c) (x+d)(x+e) -6 1 -4 (-2,0) 0 (0, 0.4) (1,0)

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Q: Solve 2 sin(2t) + 3 cos(t) = 0 for all solutions 0 ≤ t < 2π t = Give your answers accurate to at…

A: We need to solve the trigonometric equation

Q: Question 1 What is a suitable IF for solving the linear equation ty' + y = cost, t> 0 OA. B. OC 3t…

A: Given, ty'+32y=cos(t), t&gt;0

Q: 1. Evaluate the following definite integrals using the Fundamental The- orem of Calculus (b)+12+ dr

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Q: The arc length of one petal of the rose r = sin 30 is given by 1 73 2 S 2/³ TT 1 ·풍 2 S sin2 0+9…

A: We know  Length of arc length in a,b=∫abrθ2+r'θ2dθ

Q: Given: y' + y = y²(cosx - sinx) and y(0) = 2, Find C O A. 0 B. 1/4 O C. 1/2 OD. 3/4 OE. None

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Q: Suppose that lim f(x)=15 and lim g(x)=-8. Find the following limits. x-b a. lim (f(x) + g(x)) b. lim…

A: Here we have to use the concept of limits

Q: A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of…

A: Given A tank capacity is  400L , chlorine with a concentration of  0.05g/L Fresh water enters at…

Q: 1. Each of the following integrals can be found by making a substitution u for part of the…

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Q: Find the points on the surface x² - yz on the surface x² - yz = 5 that are closest to the origin.

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Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the…

A: Here we have to use the Simpson's rule.

Q: A plane takes off at an angle 6° from the horizontal. Given that the plane is traveling at 530 mph…

A: I am attaching image so that you understand each and every step.

Q: 4. At what point(s) does the curve r(t) = (sin(t), 2 sin(t) cos(t), cos(t)) intersect the yz-plane?

A: Solution: Let x= sin(t) y = 2sin(t)cos(t) z = cos(t)

Q: Use the e- definition of a limit to compute the value of the following limits: 1. 2. lim 2² – 5

A: We  will find the required  limit.

Q: f(x) = x³ - 6x² + 4, x ≥ −1. d the minimum value of the function: ve where the minimum occurs. Type…

A: Topic:- application of derivatives

Q: If f(x) = 2x(sin x + cos x), find f'(x) = f'(1) = (do not distribute) (round to 3 decimal

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