on The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its volume with respect to when Gin? Ca. 1447 cu. in/min Ob. 288 cu. in/min Od 144T cu. in/min

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

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A: Topic:  application of integration

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A: Velocity

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A: Follow the procedure given below.

Q: 2. Evaluate all of the integrals. a. [² sec² x tan x (1 + secx)² dx

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A: Here we need to cross check the given conditions are applicable to the graph of the function or not.…

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Q: 3.2.5 Test for exactness then solve. (x3+ xy2 − y)dx + (y3 + x2y − x)dy = 0

A: Given: (x3+xy2-y)dx+(y3+x2y-x)dy=0

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Q: Determine whether the series 1/4 O 1/2 3/4 + Ex=1 ( 2² - 2 +²+1) 2k+1 0 1 converges and if so, find…

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A:

Q: The pedals of a bicycle are mounted on a bracket with centre 27.5 cm above ground. Each pedal is…

A: 1) Center = 27.5 cm  Radius = 17.5 cm  Rate = 10 cycles per minute => Rate (ω) = 1/6…

Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √√(3.…

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Q: Evaluate the double integral: y LL (Hint: Change the order of integration to dy dx.) dx dy.

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A:

Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

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A: Given

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

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Q: hat is the concave up and concave down?

A: In terms of the second derivative Concave Up, Concave Down, Points of Inflection,  The graph of y =…

Q: !

A: Please refer to the image below

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Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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Q: Explain why the equation 7 = (-1,0, -1) + s(2,3,-4) + t(4,6,-8) where s, t ER does not represent the…

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: I. Evaluate the following limits x-tanx 1. lim x-sinx x-0 9

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: II. Evaluate the following integrals 3. S 3* sech³ (3¹) -dx 1+tanh (35)

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Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below

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A: In this question, we will evaluate the given limit expression.

Q: shortcuts

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Q: f(x)= 2x+5 3x-2 -19 (3x-2) f(x)=-

A: SOLUTION-

Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: Point of inflection is the point where f''(x)=0 A function is concave up in the interval (a,b) if…

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: 10. Consider the function f(x)=2x^2 +(0.4)x If the constant of integration is C=7.2, what is the…

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Q: lim (sech 2x)csch x x² +0+*

A:

Q: PLEASE SHOW COMPLETE SOLUTION.   Find each of the two areas bounded by the curves y = x^3 − 4x and…

A: Follow the procedure given below.

Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

Q: solving the following differential equations (x + tany)dy=sin ey dx

A: On solving this we will get

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A: Let's evaluate given triple integral.  There is no need to draw the graph.

Q: A) Match each equality with the letter corresponding to the property it illustrates. Responses may…

A: This is a problem related to properties of addition and multiplication. Based on the general formula…