Find the radius of convergence of the power series. (If you need to use oo or -co, enter INFINITY or -INFINITY, respectively.) 00 Σ (-1)" x" 8" n = 0

Q: dx du Sk , where u= f(x), and for some constant, k. Compute. f(2). The integral reduces to ex +1 e +...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: Ratio Test :  Suppose ∑ak be an series and            ρ = limk→∞ ak+1ak , then(i)  If ρ <1 , then...

Q: dy 2. V16 + y²

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 7 (1 -7)° (...

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Q: II. Determine the derivative of the ff. logarithmic functions 4. y = 8 log , 7x² 5. y = - 5 log , (1...

A: As per our guideline we solve only first three parts

Q: Given the function f(x) = 3 x3 + 7 x2 + 3, 8 4 -2.5 -2 -1.5 -1 -0.5 0.5 1 calculate the critical val...

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Q: following: (a) y = \f(x)| (b) y = f (x) (c) y = JF(x). f(x) y = 2 3

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Q: Question 7 dx 7-9e-2x Using u-substitution and transforming the integrand, find du. Given: A 14e2xdx...

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Q: What is f'(x) given the integral function f(x) = cos(e“)d u? %3D O rm = 3x cos(e) O f'(x) = 3x cos O...

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Q: The sequence

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Q: Graph the two equations x+y= 0, and y = - (x-1) and find the points in which the graphs intersect

A: 1. Given x+y=0y=-xtf x=0,y=0if x=1 ,y=-1if x=2,y=-2Graph passing through origin .2. y=-x-12if x=0,y=...

Q: 2) A farmer wanted to plant six different crops in a rectangular field. To protect it from animals t...

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Q: Find the equation of the tangent to the following curve at the point where x = 1 y=Vx

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Q: Use the difference a -a, to show that the given sequence (a,] is strictly increasing or strictly dec...

A: The given sequence is; {an} = n/(3n-2).

Q: d?y Find dr2 for the functlon: .3 3x +4x y=x

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Q: -1-0. 1) Write f(x). 3) Find D & R 4) Sketch f(-3t+3) 5)Find D & R for the function of point 4 2)Fin...

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Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b. x...

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Q: Find the Maclaurin polynomials of orders n = 0, 1, 2,3, and 4 and th find the nth Maclaurin polynomi...

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Q: 4. Convert SInciag) dA. aver. the region.<xyke. 2 2. .... to..pola.form. nd. then.evaluate.it.. 1/2 ...

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Q: X+ tan (xy)=0

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Q: Consider the following sequence: 5" {an} = n=1 An+1 Use the ratio to show that the given sequence {a...

A: Given sequence an=5n2n2n=1+∞

Q: b. Recall that f(x) = 2*-1-1. Graph of fi(x) = f(-x) + 2, f2(x) = f(-x+1) + 1, and fs(x) = f,(x) + f...

A: The given function,          fx=2x-1-1

Q: An isosceles triangle has an area of 21 cm2, and the angle between the two equal sides is 57/6. Find...

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Q: Differentiate f(z) = VE. Differentiate f(x) : Differentiate f(z) = (2z² + 1). 4. 5. 6.

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Q: 5x² tan( 3x³) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find . 5/2 A 18 5/2 18 5 18 D ...

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Q: tan²(x – 2) +2 sin(x – 2)4 Evaluate: lim

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Q: Find the nth Maclaurin polynomial for the function. 2x - 2 f(x) = n = 4 X +1' Pa(x) %3D

A: Maclaurin series is given by f(x)=f(0)+xf'(0)+x22!f''(0)+x33!f'''(0)+x44!fiv(0)+.... Given f(x)=2x-2...

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region above the x-...

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Q: Use sigma notation to write the Taylor series about z =1, for the function. 3Inr; 10 = 1 Σ

A: Explanation of the answer is as follows

Q: Graph the Parabola. Given: Vertex at (4, -5) and Focus at (4-1)

A: (x-h)2=4p(y-k) , Vertical parabola.Vertex - (h,k)Focus - (h,k+p)

Q: 2. Find the derivative of f(x) 3. Calculate the derivative of f(x) 2a-4+-3

A: Topic:- derivatives

Q: State whether the following series is Convergent or Divergent. n=1 O Convergent O Divergent iM:

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Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2 ...

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Q: An agriculturist wanted to plant seven different organic crops in a small field. To properly study t...

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Q: topic: calculus of polar curves 1. Find the slope of the curve r = 2cos 4Ɵ 2. Find the slope of th...

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Q: Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

A: Given ,f(x)=xx2-2Therefore,f(x+h)=(x+h)(x+h)2-2We know that ,f'(x)=limh→0f(x+h)-f(x)hTherefore,f'(x)...

Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

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Q: х — 2 1. f(x) (2? — х + 1)2

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Q: -to determine if the sequence {ne"} is strictly increasing or strictly decreasing. An an+1 Use the r...

A: 1st we have to find an  then we have to find an+1 . Then by ratio we may find it's increases or decr...

Q: sing u-substitution, the integral Jf(x)dx reduces to a new integral J glu) du. If g(u) = , evaluate ...

A: Topic:- application of integration

Q: Find the area of the shaded region in the figure. (Round your answer to two decimal places.) 120 ° 8

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Q: /4x+ – 12x² +7 xdx . Evaluate the integral A) -(4x4 – 12r²+7)/2 +c 24 © ! (21--3)/- 121+7 – 2 m 21--...

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Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral glu) du. If glu) = , evalua...

A: Given  g(u) = u+1u and  ∫f(x) dx = x + lnx-1 + C

Q: sin 3x Given: -dx_what is the appropriate formula to find the integral?- cos2(3x) (4-3 sec 3x) A du ...

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Q: an+1 to determine if the sequence {ne" } is strictly increasing or strictly decreasing. an Use the r...

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Q: x' - 36 lim 6 x+6 Vx+11-4 lim x-5 lim- 2 2-x x² +6x+9

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Q: Situation 3: Find the area enclosed by the graph of the curve x^2+8y^2+16 = 0, the x-axis, the y-axi...

A: according to our guidelines we can answer only three subparts, or rest can be reposted.