Evaluate the geometric series or state that it diverges. 00 k 3. Σ k = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 00 k O A. E k = 0 B. The series diverges.

Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x- a...

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Q: Rewrite f(x) = |4x + 4 – 3 as a piecewise function. %3D (4x + 4) -3 x if x

A: Solve by piecewise defined functions

Q: Evaluate the integral of t cot^-1 t dt . Indicate u, du, dv, and v. Full solution.

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not e...

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Q: The price p (in dollars per pound) and demand z (in pounds) for almonds are related by * = 4900 ln(2...

A: Here, the given demand function is: x=4900ln(25p2)+6500⇒x=4900ln((5p)2)+6500⇒x=4900(2) ln(5p)+6500⇒x...

Q: x²y" + 2xy' – 6y = 0 , Y1 = x²

A: The given DE is: x2y''+2xy'-6y=0 with one of the solution y1=x2. Now, dividing the DE by x2 will giv...

Q: 2-x 4x + 4x - -m(4x* + 4x – 3) + In| (2x 2x- – 3 x +1 x(x + 3)(x + 2)(x – 1) 1 (x + 3)*(x – 1)ª I dx...

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Q: A 6.2 ft tall man is walking away from a 21 ft tall lamp post. If he is walking at a rate of 4 ft/s,...

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Q: Consider the region R bounded by y = x², y = x,x = 0 and y = 0. Find the following. (a) area of the ...

A: Region R is bounded by y=x2, y=x, x=0 and y=0.We have to find the volume of the solid when region R ...

Q: A car is moving at a constant acceleration of 3.4 m/s² away from a tree. At t = 0, the car is 13 m a...

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Q: Find the measures of the angles of the triangle whose vertices are A(1,0), B(2,1), and C(1,-2). 4.

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Q: Integrate the function. dx x2+ 8x + 32 A (2x + 8}In]x2+ 8x + 32|+ C B X+4 tan + C 4 sin + C (*+4) X+...

A: First simplify then use the formula of integration and get the final result 

Q: Speedometer readings for a vehicle (in motion) at 9-second intervals are given in the table. t(sec) ...

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Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the produ...

A: Asked to answer the first question.

Q: Evaluate the integral using integration by parts. Indicate the u, du, dv, and v. Full solution.

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Q: y?sinx + y = arctanx, solve for y

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Q: ax+b The function f is defined by f (x) = , for x E R, x # - %3D cx+d' Find the inverse function f1,...

A: Given: Now,               y=ax+bcx+d⇒ycx+d=ax+b⇒cxy+dy=ax+b⇒cxy-ax=b-dy⇒xcy-a=b-dy⇒x=b-dycy-a;   a≠...

Q: dy/dx: if x=tan(x+y)

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Q: 2. In 3-space the distance d from a point P to the line L through points A and B can be expressed as...

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Q: Find the sum of the series. Σ (-1)" 32n+1 (2n+1) n = 0

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Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values ...

A: The given problem is solved below in detail.

Q: Find the area of the region bounded by the graphs of f(x)=5-x^2 and g(x)=x^2-3.

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Q: ()- In(x) C. lim %3D

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Q: 10 -10 -5 10 -5 10 5 5

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Q: Let f(x): and calculate V80-x+I f(x) dx by using integration by substitution. What was your substitu...

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Q: The average cost of producing x units of a product is C = 500e*/500 dollars per unit. What is the ma...

A: To find out the marginal cost. 

Q: A cherry with a temperature of 25 °C' was submerged in a punch of vodka of temperature 5°C. After a ...

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Q: (8) Does the series > 32n + 4 An+1 converge or diverge? Justify your answer.

A: The given series,        ∑n=1∞32n+4π4n+1

Q: H.W find the Domain and Range 1. y = v2x + 7 2. у%3D15- 2х-х? 1 x+1 3. y = 4. у3 Vx2 + 4x x - 1

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Q: 7 dx x + 1 -1

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Graph the piecewise-defined function. x-3 if xs5 f(x) = 2 if x>5 Choose the correct graph. OD. OA. O...

A: Consider the function 

Q: S sin 3xcos"3xdd

A: Given: ∫sin43xcos43xdx Let I=∫sin43xcos43xdx  ⇒I=116∫2sin3xcos3x4dx ⇒I=116∫sin46xdx

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 2...

A: We have to find the Maclaurin series for the given function                                         ...

Q: technique

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Q: H.W: Find y, y"and. y" for the fullowing -2X -xe 3- y=a Sin 3X 一ズ 2.y=eInx 4.y= In(Sex. = In (Sex +t...

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Q: Integrate the function. 8 dx V36 - 64x2 X+ C sin-1 + C -1 + C D 4 tan-1 3. B

A: Given:       ∫836-64x2dx  substitute u=4x3→dudx=43                   dx=34du         =∫636-36u2du   ...

Q: \ cosx + sinxr cos³x + sin³x 3 3. 3. cos x – sin°x |dx 3. cosx + sinx cosx – sinr

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Q: Væ = 7, – 7

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Q: A city has found that the rate its population is changing is given by p(t) people per year where t i...

A: Since p(t) represents the rate of change of population per year. and 't' represents years after 2000...

Q: Directions! show the following. f3-x x22 is dircontinuons on the interal (-,2| %3D -3

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Q: 2x+ln(x) С. у %3 Vx

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Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file

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Q: A. Solve for the Derivatives of the following functions. Final answers should be in simplified form ...

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Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

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Q: NOW YOU SOLVE THIS! Use Table of Values and Graphing to determine the limits of the following functi...

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Q: a) A guy picks up a positive rational number and multiplies it by itself three times i.e. he calcula...

A: A guy picks up a positive rational number ab

Q: If y, and y, are linearly independent solutions of ty" + 3y' + te²"y = 0 and if W(y , y2)(1) = 3, fi...

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Q: VE 1+ V=dx = a[Vx= = In (1 + V=)] + e 16.

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Q: y" (t) – y' (t) - 2y (t) = 12t - 6e2t; y (0) = 1; y' (0) = 0 |

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