Consider the following sequence: {an} = an+1 Use the ratio an - to show that the given sequence {a, } is strictly increasing or strictly decreasing. Sequence is strictly increasing decreasing GO Tutorial

Q: Determine whether the alternating series converges. 51n k (-1 k k=3 O The series diverges. O The ser...

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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: Please see the image to see the given. thank you (a.) the critical numbers of f (b.) all relative e...

A: To find: (a.) the critical numbers of f(b.) all relative extrema of f(c.) the intervals on which f i...

Q: Question 12 If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+') + C, find the exact val S ...

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Q: The radius of a right circular cone is increasing at the rate of 6 cm/sec while its altitude is decr...

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Q: 2. In each of the following, find fyzz, fæyx, fryz- 2. f(x, y, z) = ln(xyz) + z² tan-1(e"y)

A: Given

Q: (-1)"n! 3. (a) Test the series for absolute convergence. n" n=1 2 4 2n-1 (b) Prove that the series 1...

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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: Solve the following ODE. y" + 2y" – y- 2y = 9 - 123 NOTE: Write arbitrary constants as c1, Cg, and c...

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Q: Use the formula for the binomial series: (1 +x)" = 1+ mx + + + -1) %3D = I+ Ei to obtain the Maclaur...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 6 Pa(x) =

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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: Differ entiare Y = \og (coc V; ) Ditterentiare り; x& cos cos"s

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Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z9 = 1 k =

A: The given function is 3ln(x);x0=1.

Q: Does the following power series converge for all real values of x? (-1)"x" n n=1 It converges for al...

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Q: A. Evaluate the following integrals 1. 2. L. 3. , e*dx dx dx -1 x2/3 4. SE tanodo -4 dx

A: solution:-Q.(4) ∫-∞π2tanθdθsolving the improper integral=limt→-∞∫tπ2tanθdθ=limt→-∞∫tπ2sinθcosθdθ=lim...

Q: sin(2a)dx + cos (3y)dy 3 0, у(т/2) — п/3 ||

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Q: This problem is about evaluating the integral V2/2 1 dx - x2)3/2 (1 – To start, one would make a sui...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 k+1 Σ (2k –...

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Q: ry' – y = x²e=z

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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: B. Directions: Expand t Scoring Rubric: 3- The final ansv 2- The final ansv 1- The final ansv 0- No ...

A: = (12q+4r)12  Binomial Expression:(a+b)n =∑n=0nni a(n-i) bi(12q+4r)12:  a=12q, b=4r=120(12q)12-0(4r)...

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: Find the radius of convergence and the interval of convergence. 00 k(k + 1) k=1 1) First apply the R...

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Q: One model for the spread of a rumor is that the rate of spread is proportional to the product of the...

A: Let's find. 

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: Please see the attached image to see the given. thank you  (a.) the critical numbers of f (b.) all ...

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Q: Explain briefly why the function f(x) = e" – x³ – 8 eIntermediate Value Theorem. Use IVT to show tha...

A: We will use the Intermediate value theorem. 

Q: Watch the video on partial fractions with a repeated irreducible quadratic factor e and thevideo on ...

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Q: The graph shown is f(x) = sin x. What is the integral that defines the area under this line between ...

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Q: Find: 6x 3x2-7x+4 dx ---

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Q: xy' + (x + 1)y = x, y(ln(2)) = 1

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Q: 3/2 X2 dx

A: 1.∫x32tan-1(x) dxlet x=tdiff o.b.s12xdx=dt dx=2t dt∫t3tan-1(t) 2t dt=2∫tan-1(t) t4 dtwe know that ∫u...

Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel.

A: According to question,Given equation of lines,4x - 3y +12 = 08x - 6y +15 =0

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: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y ...

A: As per our company guidelines we can answer only three subparts question at a time, but if you need ...

Q: 2) Which of the following sequences are summable. If the sequence is geometric, find the sum: a) a; ...

A: a) a1= 5/4 a2= 25/16 a3= 125/64 b) a1= 11/6 a2= 15/11 a3= 19/16  

Q: In general, a partial fractions integral with a repeated irreducible quadratic factor will result in...

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Q: If the solution to e2x sec2(e2x+1)dx is equal to k tan (e2x+1) + C, find the exact value of k. 1 A 2...

A: This question can be solved using the concept of integration by substitution.

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: Show that for all positive integers n, 13 + 2° + ...+ n³ = (1+2+3+ ...+ n)?

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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: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: Find the nth Maclaurin polynomial for the function. 3x - 5 (x) = n= 4 x + 1 Pa(x)

A: The given function is; f(x)=(3x-5)/(x+1); n=4.

Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z0 = 1 k =

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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...

A: This is a problem related to geometry. For parallelogram opposite sides are parallel to each other. ...

Q: 15. Scott Fallstrom once Epoke with his kids on the first day of the month of April about allowances...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: Explanation of the answer is as follows

Q: Question 1 dx The integral can be re-written as A lim (-1+2 y 1-m m - 0 B none of the choices lim (2...

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Q: 5x? tan( 3x³) dx. fu= 3x³, then the resulting integral is f(u) du. Find A Given: 4 A none of the cho...

A: Topic:- application of integration