Using two infinite series whose convergence/divergence is known, determine whether the given series is convergent or not. 10 Σ n2 + 2n + 1

Q: ydy 4. +4y+11

A: ∫1u2+a2 du =1a arc tanua+C ∫1u du =ln(u)+C

Q: Functions f and g are defined by g(x) = V-x+4, x<4; xeR h(x) = 2e*, x20; xeR (a) Find the composite ...

A: g(x)=-x+4, x≤4h(x)=2ex, x≥0a)   (h∘g)(x)    =h(g(x))     =h(-x+4)     =2e-x+4 ⇒(h∘g)(x)=2e-x+4   Dom...

Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: larger slope y =

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Q: Determine if the improper integral converges and, if so, evaluate it. dx | 8+x Write F if the integr...

A: We will evaluate the integral.

Q: In a college meal plan you pay a membership fee, then all of your meals are at a fixed price per wee...

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Q: ve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" + y = 0, y'(0) = 0...

A: Topic:- differential equations

Q: Solve the given differential equation by undetermined coefficients. у4) — 2у" + у" %3D еx + 1 2 x vx...

A: Here, the characteristic equation is     m4-2m3+m2=0. Now,              m4-2m3+m2=0⇒m2m-12=0⇒m=0  or...

Q: The height of the cylinder is 8 inches.   We'll be analyzing the surface area of a round cylinder ...

A: We have to find the domain, inverse function and evaluate r(275).

Q: dy dz 2. x+1 y+1 z+1

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Q: f(x) = 2x/4x² + 2 (A) Find all critical values of f. If there are no critical values, enter -1000. I...

A: In order to find the critical values, increasing interval and decreasing interval of f(x). We must d...

Q: Problem 7. (1 point) Let f(x) Then (fo g)(2) =, (fo g)(x) =|| = 2x + 4 and g(x) = 5x2 + 5x.

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Q: 3.)lim-). 1 z→i`z-i z2+1

A: Given query is to find value of the indicated limit.

Q: 5. You started with a pool that was 15 feet by 20 feet. What is the area of the pool without the pat...

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Q: Xy +Sx+5?= 2

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Q: 1 dx x2 + 1

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Q: A company estimates that it can sell 3,000 units each month of its product if it prices each unit at...

A: We need to maximize profit.

Q: 8. For the quadratic function f(x)=2x² – 24.x+90 (a) Complete the square to put the equation into a(...

A: Given query is to find the the vertex form and the minimum value of f.

Q: roblem 1 a) Find f o g.and g o f together with their domair f(x) = x³,x € R ; g(x) %3D

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers ...

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Q: a comma-separated list of equations.) Find all horizontal and vertical asymptotes (if any). (If an a...

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Q: (a) Find all the zeros of the polynomial function P(x)=x² +6.x+ 20. Use a graph to help get started....

A: Explanation of the answer is as follows

Q: Kirk's Convenience store sells 15 different brands of chocolate bars. Of these, 6 brands contain nut...

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Q: 8) Determine whether the series is convergent or divergent. If it is convergent, find its sum. 1+ 2"...

A: Using root test for checking series is convergent or divergent.  And for finding sum of series , we ...

Q: 11. Write an equation for the result of shifting the graph of y=xv3+x to the left 2 units and then d...

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Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.  

Q: Please do 15 and 17

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Q: y = (13x – 2x+1 - 1]) find the second derivative x+5

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Q: J-x if x<1 (x+1 _if x21 7. If f is the piecewise function f(x)=- (a) Evaluate f(-2) and f(2). (b) Sk...

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Q: Let T2(x) be the 2nd degree Taylor polynomial for the function f(x) = 7 + xe-2* centered at a = 0. F...

A: Given,            The function is fx=7+xe-2x centered at a=0.To find : The Taylor polynomial of 2nd ...

Q: ydy y +4y+11

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Q: following functions and determine the type of its discontinuity (Removable, Jump, Infinite) f(x) = 5...

A: given function  f(x) = 5/x-4

Q: Solve the given differential equation by undetermined coefficients. у" + у'+ у 3x sin(x) y(x) =

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Q: Problem 3 a) Suppose C(r) is the area of a circle whose radius is r, and S(r) is the area of the cir...

A: Firse make the digram then find the area of square and circle and divide and find the answer.  In 2n...

Q: A retail company estimates that if it spends x thousands of dollars on advertising during the year, ...

A: We will find the marginal profit. 

Q: 3. Find the number of paths from A to B, travelling along the lines, downward or to the right.] A B

A: Using combinatorics =(m+n-2)!/(n-1)!(m-1)!

Q: The profit (in dollars) from the sale of x lawn mowers is P(x) = 50x - 0.05x² - 650. (A) Find the av...

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Q: For the following exercises, draw the region bounded the curves. Then, use the disk method to find t...

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Q: and A-1 true fals 412

A: Solve the matrix to find the inverse

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

A: The given integral,      ∫33316x-33dx

Q: Differentiate f(x) = //2x² 4х + 2 %3D - 02() x-1 2x2-4x+2 x-2 2 2x2-4x+2 x-1 2x2-4x+2 x-1 2 2 2x2-4x...

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Q: Find the maximum and minimum values of g(x) =1+ x + x2 + x³ + x4 + x on the interval [0, 2].

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Q: x+4, for x - 2 ... (A) Select the correct choice below and, if necessary, fill in the answer box to ...

A: Given information: The function is f(x)=x+4    for x&lt;-2x+2  for x&gt;-2 (a) To find:  limx→-2+f(x...

Q: You are the Director of Infrastructure Management at the Nash Telecommunications Company. You are ta...

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Q: Given the demand function D(p) = 125 – 3p, Find the Elasticity of Demand at a price of $4

A: Topic:- demand and it's elasticity

Q: Consider the following equation. xy + 2x + 3x² = 8 (a) Find dy/dx by implicit differentiation. y' = ...

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Q: sinx - cosx + 1 sinx + 1 %3D Hint: the conjugate of the denominator XS200S sinx + cosx - 1 cosx is s...

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Q: Let f(x)=x^3 + 5. Explain why f(x) is invertible, then how all steps in the derivation of a formula ...

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Q: A manufacturer believes that the cost function 3 C(x) = a +36x +920 2 approximates the dollar cost o...

A: here, the given cost function is: C(x)=32x2+36x+920

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 3 , da = x2 – 9 -

A: Given query is to find the value of the integral.