Find the centroid of the region in the first quadrant bounded by the given curves. y = x?, x = y7 (X, y) =

Q: 2x² + 1 Find the lim, f(x) where f(x) : if xs -5 x – 3x-2 if x > -5 x-5* -122/25 O -72/25 O -80 None…

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Q: Find all relative extrema of the function. Use the second derivative test to determine the extrema.…

A: We will find the relative extrema and the value of f"(2) as following. The function given f(x)=x^2…

Q: Idx/(1-2x) = 1/2 In]1 -2x + C Select one: O True O False

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Q: Consider the following. u = (1, 2, -3), v= (5, -1, 0) (a) Find the projection of u onto v. (n. 264)…

A: Find your answer below

Q: Using trigonometric substitution, the integral / 2-x² dx x4 is equivalent to x/3 A 8 sin?0 cos?0 de…

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Q: Find the gradient of the function at the given point. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

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Q: The edge of a cube is changing at the rate of 0.2 cm/sec. How fast is the volume of a cube changing…

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Q: Graph the equation below. Choose the correct graph. y = 5.5* OA. O B. OC. OD.

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Q: (Rounded to the nearest hundredth) Use the cylindrical shell method to calculate the volume of the…

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Q: Solve the following initial value problem. dy 1 --X, x> 0; y(6) = 3 dx x2

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Q: ctangular storage container with an open top is to have a volume of 10 m3. The length of this base…

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Q: uantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer…

A: Since we are given with the multiple number subpart answered according to the guidelines

Q: vo Variables 4)dr + (2r. (2. 4x)dı

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Q: Given the function below find the value of f(-4). * if x -5 2x² + 1 f(x) = O -67/16 None of these O…

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Q: 'ind the exact length of the curve x = t sint y = t cos t or 0<t< 1. ou may use the following result…

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Q: Suppose the position of a particle is given by parametric equations x(t) = 2t2-1 and y(t) = 3t3. (a)…

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. 4x? + 9x?…

A: The given equation,     4x2+9x2=25, 2,-1

Q: Recall: v = can be written as v = ai + bj + ck , where i = , j = and j: . Let v = – 2i + 5j – 4k…

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Q: e" + e¯ cosh(r) : e - e sinh(r) 2 Use our rules for differentiating e" to show that cosh'(r) =…

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Q: (b) If a > b and c > 0, then ac > bc.

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Q: Find the dimensions of a rectangle with area 216 m2 whose perimeter is as small as possible. (If…

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Q: A 400-lb cable is 250 feet long and hangs vertically from the top of a building. How much work is…

A: A 400-lb cable is 250 feet long and hangs vertically from the top of a building. ρ=mass per unit…

Q: 4. [V40-4v-v² dv

A: Please see the answer below.

Q: |(4csc2x - 3sec2x) dx = -4cotx - 3tanx + C Select one: O True O False

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: Evaluate xe*dx. -3

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Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship…

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Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: topic - application of derivatives

Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

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Q: Vx- 2 Evaluate lim x-8 x2-7x-8 O 2/7 None of these O 1/9 O 1/12 O O o O

A: The given limit,     limx→8x3-2x2-7x-8

Q: Find the limit. lim Vr+3

A: Question 1,Given,            limx→6x+3

Q: Question Using Trigonometric Substitution, evaluate: S e4*/1+ e2xdx Your answer

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

Q: A bacteria culture is known to grow at a rate proportional to the amount present. After 60 minutes,…

A: We will find the number of strands of the bacteria originally in the culture as following. After 60…

Q: Find the gradient of the function at the given point. w = x tan(y + z), (5, 13, –10) Vw(5, 13, -10)…

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Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area

Q: – ydy (у+ 1) — у+1

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Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x +…

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Q: Consider the following. x = t, y- In(t) (a) Eliminate the parameter to find a Cartesian equation…

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Q: Evaluate each of the following indefinite answers in simplest form (factored form) 3dt 1. (2t +8) Jt…

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Q: xdx Evaluate (x²-2)5

A: We have to use rules of integration to solve the question

Q: Select

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Q: The shaded region shown below is bounded by the functions f(x) = -4x? + 10 and g(x) = x + 6 and the…

A: area

Q: TRUE OR FALSE 1. ∫(4csc2x - 3sec2x) dx = -4cotx - 3tanx + C 2. ∫6x2e2x^3+1 dx = 3e2x^3+1 + C 3.…

A: We have to find the solution

Q: Consider the function y = 3(square root of x) + 8. What is the value of C in the interval [4, 9]…

A: First we will find fave

Q: Find the following limit by evaluating an appropriate definite integral over the interval [0, 1 lim…

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Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: Consider the function y = 5x4-4x3-3x2+8x-12. What is the average value of the function on [-3, 1] ?

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