2. For a given perimeter, what is the ratio of the length to the width of a rectangle that will have the maximum area? a) 1:1 b) 1:2 c) 2:1 d) 3:1

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A: To evaluate the integral given below. To check theanswer by differentiating.∫16t-6 et dt=?+C

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, the total…

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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A: Answer is 9π c. u.

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A: We can solve this problem as follows:

Q: Consider dx x1/2 + x2/3 Find the integrand in terms of z. A [62²dz 1+z² B none of the choices 6 z5…

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Q: A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6…

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: please include un your solution the computation for the points of intersection. Thank you

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Q: -2 What is the value of the definite integral e* dx? -4

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Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

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Q: termine the derivative of the following implicit function on a separate sheet paper, assuming that…

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: Which of the following describes the partial fraction decomposition of a rational function of the…

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Q: Which of the following is true? * f (x, y) = x³ - 2xy + 3y² fx = 3x² - 2y + y³; fy = 6x Option 1 f =…

A: The given function is;  f(x,y)=x3-2xy+3y2.

Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: Given: 4x+8y=8, y=0 x-axis, x=0 y-axis So, the bounded region is as shown below. Apply the disk…

Q: -1 33x So 43x dx 0 O 0.6698 0.6670 O 0.6699 0.6671

A: Solving the definite integral by using substitution.

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A: x+y^3=2c(x y^4) differnetiatiate with respect to x

Q: 1 Evaluate the given limit of the following: lim [(x² - In(x + 1)) cotx] x-0

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Q: Using Rationalizing Substitution · √ √x + 10 x+2√x +In(√√x-1)² +C °√x (√x + 4) + In (√x - 1)² +C…

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Q: Evaluate the definite integral I. 1 = [₁² [(e-x + 1) dx -1 I =

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