Write the given decimal as an infinite series, then find the sum of the series, and finally, use the result to write the decimal as a ratio of two integers. 16) 0.2929292...

Q: dr 1/4( In 4) o 1/( In 4) o In 4 In (4) 1/4

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Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: (-2,0,5) and (–1,2, 3). Find an equation of the sphere whose endpoints of a diameter are

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Q: 3/2 x*(G²- x²) %z

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Q: If f(x) = 8+r dt, find f(1).

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: we are given the function f(x)=cos(x) and the interval -π3,π3.The function f(x) is continous on the…

Q: Find f'(2).

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Q: Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb…

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Q: (п+1 c) Σ-1 3η2 b) En=1(-1)" (41) Inn a) En=3 (in (Inn).

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Q: The Mean Value Theorem states: For any function, f, differentiable on (a, b) and continuous on [a,…

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Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: Determine the area of the glven reglon. y = x + sin x 3- 2- Step 1 Note that for the given reglon, x…

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Q: 6. v(y) = In (y² – 8y – 1)

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Q: Find the length of the curve. 9) The spiral r = 202, 0 s 0 s 2^/3

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Q: dr Let A be the area of a circle with radius r. If dt dA = 2, find dt when r = 5.

A: Given :drdt=2r=5

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: A particle moves with its position given by z = cos(t) and y = sin(), where positions are given in…

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Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: 3 roblem 4. The third term of a geometric sequence is 9, and the common ratio is Find the fifth…

A: Given problem:- The third term of a geometric sequence is 9, and the common ratio is 3/2   Find the…

Q: x2 - 6x + 8 lim x--2+ x3 - 4x

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Q: Use the chain rule to find the derivative of 3(– 82° – 2=")" - You do not need to expand out your…

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Q: dy 5. Vy -1

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Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: 9.

A: Given,  y=2x+x4-9x+3

Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: a. 0 =-45 → graph type = b. r= 8-8cos0 graph type = facing up/down/left/right? loop length = c. r=…

A: (a) θ=-45°Graph type straight linesymmetry along first and third quadrant     (b) r=8-8cosθgraph…

Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Evaluate this double integral. Avoid integration by parts. Hint: Can you reverse the order of…

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Q: Problem 3. A stone is dropped in a lake, creating a circular ripple that travels outward at a speed…

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Q: Find the Yalue + Cas

A: Using inverse trigonometric formula achieve this expression

Q: s @ = 135° a solution to the equation sine = cos 0. Justify your answer and explain the approach you…

A: Given query is to find that statement is true or not.

Q: Evaluating Indefinite Integrals - Partial Fraction Decomposition Suppose we want to evaluate the…

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Q: Find the area of the shaded region. y y = x2 + 1 ... y = x -1 2

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: and y=x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the solid…

A: Given :-region bounded by y=x2  ,  y=x+2revolving about the x-axisusing washer/disk…

Q: Find the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

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Q: 18. Find xV4x -3 dx 18. SxV4x - 3 dx

A: Use substitution to solve

Q: Set up and simplify the surface integral ∬S F dS where F(x,y,z) = 2xi + yzj - √y k and S is the part…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: The three basic trigonometric substitutions are in the table below. Integral Contains Try using…

A: We will solve the integration.

Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: 10 %3D1

A: Formula Given

Q: 2- A radio station conducts a poll about gun control. It invites listeners to call one phone number…

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Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: FH is perpendicular to AC In the figure, AC is diameter. If EF = 3 and FG = 2. Find GH. E G EH is…

A: Similar triangles: Similar triangles are triangles with the same shape but different sizes. Similar…

Q: nd lim l Nx-3 and simplifu X-79

A: Given query is to find the limit of the expression.