3. Use the Comparison Test to determine if the series 5n Cos 2n n³ + n² + 1 n=1 converges or diverges.

Q: Find the total differential. z = e-X tan(y)

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Q: dx sin? - cos 2

A: Here, the given integral is: I=∫0πsin2x2cos7x2dx Substitute x2=t⇒x=2t⇒dx=2dt as x→0⇒t→0 & as x→π...

Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3 sin(x...

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Q: lim, s0¤(t) = 1? Оа. "+а — 0, z(1) — 2. 0, г(1) — 2. ОБ. — - 0, 2 (2) — 1. Ос. - 2г — — 0. 0, æ(1) 0...

A: To determine which of the following initial value problems has a solution xt.limt→∞xt=1a x'+x=0, x1=...

Q: If the second derivative of the equation of a curve is equal to the negative of the equation of the ...

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Q: A company produces a special new type of TV. The company has fixed costs of $453,000, and it costs $...

A: We have to find the price that can maximize the profit.

Q: If f(x) = (2x + 8)-', find f'(x). Find f'(2).

A: topic - derivative of a function

Q: A rectangular box with a volume of 64 ft is to be constructed with a square base and top. The cost p...

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

A: Given query is to simplify the expression  

Q: Your are driving away from Detroit. Your distance​ (in miles) away from Detroit x hours after​ 12:00...

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Q: uestion 6 of 11, Step 1 of 1 5/11 Correct Consider the function f(x) = -x' - 6 on the interval (-4, ...

A: Given query is to find absolute maximum and minimum.

Q: (a) f(x)= Jx-6 (b) g(x)= /7-x (c) h(x)=V1-x²

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: A water tank in the shape of an inverted circular cone has a base radius of 4 m and height of 6 m. I...

A: A water tank in the shape of an inverted circular cone has a base radius of 4mand height of 6 m. If ...

Q: sinh (5) = %3D (A) 5 + V26 (B) In(5 + /24) (C) In(5 + v26) (D) 8. (E) 5

A: Use the definition of hyperbolic of sine function. 

Q: у 3 cos (4x — 19)

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Q: 3. Solve the following equations over all real num V2 sin(-x) + 1 = 0 a. |

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

A: To find: The Maclaurin series expansion of f(x)=ln(3-2x). Concept used: The Maclaurin series can be ...

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: 221 writc a formnla for the function y =f cx) whose is shown fig: 2.

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Q: Given polar curve r = −6 sin(θ) do the following. (a) Find the Cartesian equation for this curve. (b...

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Q: ☺ Find tue indefinile intgrel. cos (5@] do

A: ∫un du = un+1n+1+C ; where, 'C' is an integration constant.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y ...

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Q: 7 Type equation here.

A: topic - indefinite integral

Q: S 12x²Vx3 + 7dx

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

Q: Replace ? with an expression that will make the equation valid. d. x* +5 = ex +5? dx The missing exp...

A: Consider the expression  ddxex4+5=ex4+5   _

Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: (a) e2tsin (wt +t/6)

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Q: Find the derivative of f(x, y) = e*y + eY at the point (1,3) in the direction of the vector

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Q: Σ 7 2 n n=1 п (In? п + 1) 8

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Q: Use long division to divide and use the result to factor the dividend completely. (5x2- 3x-14) (x- 2...

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Q: True or False: If we use substitution the substitution x = tan 0, then, the integral dx 1 + x2 trans...

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Q: y' + 3y = 5e2x – 6; y(0) = 2

A: since you have posted multiple question in this question which are not interlinked so i have solved ...

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. 

Q: ſcos^4 (2t) dt * O 3/2 t + 1/2 sin4t + 1/16 sin8t + C O 1/4 (3/2 t + 1/2 sin4t + 1/16 sin8t )+ C O 3...

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Q: i- graph and Rined Demain and Range for yz sin'x- 3 ーhn Hi-z+ 3x3-5 2. - graph apel find Df f Rf for...

A: 1. y=sin2x-32. limx→∞4x3-2x2+13x3-53. y=-5sin2x Note:      Multiple questions are given, we are answ...

Q: dy + 4y = 8 dy d. x- dx = (x – y)² %3D a. dr dy e. da dy + 4y = x? %3D b. = V1+x2 %3D dx dy dy c. dr...

A: This can be solved as follows:

Q: Section 4.1 p. 363/365 # 40 Solve the following initial-value problems starting from y(t = 0) =1 and...

A: We have to solve the initial value problem and draw solutions.

Q: Let f (x, y) = e^x (sin(y) +1) and use the point P (0, (pi/2)) a. Find the gradient of f at P. b. F...

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Q: Qal AIf fo =Sx-ul, gca)=x fin d fogcx) Then graph it determine domain and range.

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

Q: 2. (а) Find the function P(x) = a +b cos(n x) +c sin(nx), which interpolates the data 0.5 1 y 4 (b) ...

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Q: I Find the second derivative(y") of the following functions and simplify the final result 1. y = x –...

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Q: By substitution u = x² + 5x, the definite integral (2x + 5) In (x + 5x) dx becomes Select one: O Non...

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Q: TT(e-1) В. 2.

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Q: Solve the differential equation by using integrating factors. xy' = 3y + x2

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Q: Given the data points (0, 2), (1, 1), find the following: (a) The straight line interpolating this d...

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Q: Let f(æ) = (4x² + 5æ + 2)° f'(x) =

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Q: It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 4 m. Find ...

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Q: MODULE IN BASIC CALCULUS IV. Exercises 1. Determine the general antiderivatives of the following fun...

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Q: 4y2 = 3. Maximize Q= xy, where x and y are positive numbers such that x+ Write the objective functio...

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

A: Given:   ∫17x-1x2+16 dx