1. A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4 in/min, respectively. If the height is always the twice the radius, find how fast the volume of the tube is increasing when its radius is 10 in.

Q: 5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and…

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Q: Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20…

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Q: Given the space curve r(t) = (2 cos 2t, 2 sin 21, 31), find the unit vectors, 4 B

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Q: Use partial fractions to find the power series of the function: n=0 4x + 41 (x − 2)(x + 5)

A: To find power series for the given function.

Q: The after price tax on your new shiny car is $25,989.60. If a 4% sales tax was charged what was the…

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Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: To find v(t) ,s(t) and a(t) for the given position vector r(t).

Q: x+2 3.) (x²-1)(x²+1)² of factor. dx; Solve by using partial fraction. Indicate the type

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Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

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Q: In Problems 17-26, solve the initial value problem. dy y(0) = √3 dx y' = x³ (1-y), 1 dy 2 dx dy…

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Q: Initial speed is not 98 ft/s. What is the initial speed

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

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Q: 2 cy² = x² + y

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Q: aluate the following integral in spherical coordinates. This integral calculates the volume of the…

A: See this solution in below

Q: 8. Solve the differential equation: d'y 3: dx² -4+y=0 dx

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Q: Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 5.4%…

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Q: QUESTION 2 The equation ut = 2uxx is O a partial differential equation in one variable O an ordinary…

A: Given: ut=2uxx

Q: Evaluate: AT -dx B. 이집 는 d 를

A: Evaluate the integral ∫0πxsinx1+cos2xdx

Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: Which of the following statements is/are true based on the graph of the function f(x) = -2(-x-²) +…

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Q: 3. Translation: (x,y) → (x-6, y + 4) 5 -5 -5 Y C B X D 5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: J 4 sin xecos* d.c

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

Q: A solid of revolution is formed by revolving about the x- axis the region bounded by the curve y √2x…

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Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…

A: To find domain and range of the given function.

Q: The equation u, 2uxx is a partial differential equation in one variable an ordinary differential…

A: Here we will find the correct option,

Q: Evaluate the following limit. t sinj+ sin = 1+ k t -k π lim costi-5 1-x

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Q: 4. 4 1 [x²ydxdy 20

A: I have stated the used formula in the solution

Q: Trig Substitution: For the following integral, which trig substitution is needed? O Tangent Sine…

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: Which of the following functions describes the graph of g(x)? -10- + O g(x)= O g(x)= (2) 2²-8 2²-8…

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Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

A: Please see the below picture for detailed solution.

Q: Determine the intervals on which f'(x) is positive and negative, assuming that given figure is the…

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Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

A: Overpass is in the shape of a semi ellipse. 15 feet height at the center that means distance between…

Q: 2 The function f(x) ==, x0, is one-to-one. X Find an equation for f(x), the inverse function. ...…

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Q: 17. Evaluate: √4x² - 4x + 5 dx A. √4x² - 4x +5 +In(2x+1+√4x² - 4x + 5) + C 8. √4x² - 4x…

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Q: 인 여 प्रि sin K K K

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Q: a T c. 10 ml Convert the following (us

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Q: Evaluate: fx 3* dx if a is equal to the first digit and bis equal to the second digit of the sum of…

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Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: The stopping distance for an automobile (after applying the brakes) is approximately F(s) = 1.1s +…

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Q: The direction field of the DE y' + ye³x+7= -2y² will have a line segment with positive slope at the…

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Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

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Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1

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Q: 47. Suppose cote>0 and sec 0 <0. In which quadrant could terminate? (A) Quadrant I (C) Quadrant III…

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Q: As per the trigonometric substitution x = sin(0), the following triangle is obtained. cos(0) Submit…

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