Show whether each of the following series diverges at the end-point (s) of the interval of convergence: n!(r+3)" (b) n=1 (c) En" (x + 3)" n=1

Q: What’s the derivative ? f(x) = xe^-x3

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Q: (4) Let S be the surface parametrized by I =r cos 0 y = r sin e 2 = 30 where and 0<r< 4 Evaluate the...

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Q: Calculate the volume of the solid obtained by rotating the area bounded by f(x) the x(x + 1) X-axis,...

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Q: Sin/cos

A: Given query is to simplify the expression.

Q: 2) Find tue indefinite inpegrel W V 2w +5 dw

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Q: Solve the differential equation y y' = - + sin sin ()

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Q: Solve the differential equation y - X) - + sin + sin (* y'

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Q: rove that the given equation is a solution to the given DE: 5. x = 2t + C; y = Ct + 3 ; 2(y')² – xy'...

A: Topic:- application of derivatives

Q: 1/2 dx r2)2

A: Given problem:-

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm³/...

A: Let the radius of the sphere is r then given drdt=4 mm/secand diameter is 2r=40 mm

Q: The arc length along the parabola y = x² from (1,1) to (2,4) is given by which of the following inte...

A: Let's find. 

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

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Q: Find an арprozimation of 1000 i=1

A: Find your answer below 

Q: 1. f(x) 16x? – 4x +5 %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: 2 dx х3.4 а. x2.2

A: ∫1x2.2-2x3.4dx∫x-2.2dx-2∫x-3.4dxFormula: ∫xndx=xn+1n+1+C

Q: 1. tan(8) cos(8)

A: Given query is to simplify the expression  

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (x) = 5x – 4

A: Note:- These are multiple questions and according to our company guideline we can do maximum 1 quest...

Q: The cost of producingx units is given by C(x) = 32000 + 1.7x + 20x dollars. Find the value of x that...

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 – x² and ...

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Q: Evaluate the given integrals. 3x?dx 1. S 2х4-1 2 dx 2. S tan x(5+ln sin x) 3. Seš(6– ei)" dz 1 4. S ...

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

Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx ...

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x...

Q: (b) Determine the equation of the line normal to f(r) =r²- 4r +5 at z = 1., Hint 1: The normal line ...

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Q: Question 1 Find the area bounded by the parabola x = y? and y = x-2. Answer in decimal form.

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Q: A large corporation with monopolistic control in the marketplace has its average daily costs, in dol...

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Q: Find the solution of the differential equation with the given initial condition. dy 2xez? y(1) = 2 d...

A: This question is based on solution of differential equation.

Q: Find the derivative or y'. Show your step by step solution.

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Q: differential equation .2x 2

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y = x...

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again diffe...

Q: 83. The acceleration of a particle moving along the x-axis is given by a(t) = (t- 8)sin t for 0 <IS ...

A: we know a(t)=d(v(t))dt where a(t) is the acceleration, v(t) is velocity and t is time. The particle ...

Q: Find the first derivative of the given functions: 1.)  x=(Arcsinh(1-b))2   2.) y=e-xcosh ln(x)

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Q: To evaluate the integral / V16 – x² dx, we use Select one: O x = 4 sec 0 O x = 4 sin 0 O x = 3 sin 0...

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Q: Exercise 2 Find symmetric equations of the normal line to the surface 4 + y – 162 = 0 at (2,4,2). (a...

A: Given surface is     4x2+y2-16z = 0We will find the symmetric equation of the normal line to the sur...

Q: sin? - cos' 2 2 zdx 2.

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Q: Consider f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(x)= ------- Bas...

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Q: „J: Evaluate the integral (4x + 1) In x dx . Evaluate the integral Sou 6 tan x sec* x dx 1: Evaluate...

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Q: Use the degree 2 Taylor polynomial for f(x) = x centred at a = 1 (from question 3) to find an approx...

A: Given is the question of taylor series expansion.

Q: Using f (x) = In(3 – 2x), find the value of L and calculate the radius of convergence of the series....

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Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y)...

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Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2x)

A: Here we have to find the maclaurin expansion of the given function.

Q: 8. Using (4.6), find the polynomial P2(x) that interpolates the following data. In each case, simpli...

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Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the...

A: The given curve S is parametrized by: R→(u,v)=uv,sin u,cos v Now, to find the equation of the tangen...

Q: 20x² Evaluate the integral: -dx V64 – 72 (A) Which trig substitution is correct for this integral? 8...

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Q: Question 6 - P Consider a room in the shape of a cube, 4 meters on each side. A bug 4 m at point P w...

A: according to our guidelines we can answer only first question and rest can be reposted. 

Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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Q: S 12x²Vx3 + 7dx

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

Q: 2sin x -1 2. y = cosx+ 2

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: Lesson 13 Find the derivative of the following functions. Show your solution. 1. y = x' cos x 2. y s...

A: This can be solved as follows:

Q: True or False; In the partial fraction decomposition, x + 8 A В D + x(x – 1)(x + 3) х — 1 x + 3 - we...

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Q: A container with square base, vertical sides, and open top is to be made from 1000 ft2 of material....

A: Let the container has a base side "x" and height "y"

Q: 1. Determine if if r2 /2r is differentiable at r 2.

A: First check for continuity then the derivative if both exist then function is differentiable.