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8.arectangular Box Having A Square Base and Open at The Top Is To Have

The document appears to be a student exam containing 10 multiple choice questions related to calculus concepts such as area, volume, limits, derivatives, and centroids. The questions cover topics like finding the volume of revolution, limits of functions, maximum profit problems, and geometric shapes. No answers are provided, just the student's name, ID number, and a space to record their score.

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Pete Bas
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57 views1 page

8.arectangular Box Having A Square Base and Open at The Top Is To Have

The document appears to be a student exam containing 10 multiple choice questions related to calculus concepts such as area, volume, limits, derivatives, and centroids. The questions cover topics like finding the volume of revolution, limits of functions, maximum profit problems, and geometric shapes. No answers are provided, just the student's name, ID number, and a space to record their score.

Uploaded by

Pete Bas
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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NAME:____________________________

STUDENT NO.:_____________________
DATE:_____________________________
SCORE:____________________________

DIFFERENTIAL AND INTEGRAL CALCULUS


Show your solution!

_______________1. The area bounded by the curve y^2=12x and the line x=3 is
revolved about the line x=3. What is the volume generated
a. 186 b. 179 c. 181 d. 184

_______________2. Find the area bounded by the y-axis and x=4-y^(2/3)


a. 25.6 b. 28.1 c. 12.8 d. 56.2

_______________3. Three sides of a trapezoidal are each 8cm long . How long is the
fourth side , when the area of the trapezoid has the greatest value.
a. 16cm b. 15cm c. 12cm d. 10cm

_______________4. Given the following profit versus production function for a certain
commodity:
P= 200000-x-(1.1/(1+x))^8
Where P is the profit and x is unit of production. Determine the maximum profit.
a. 190000 b. 200000 c. 250000 d. 350000

_______________5. Water flows into a tank having the form of a frustum of a right
circular cone. The tank is 4m tall with upper radius of 1.5m and the lower radius of
1m.When the water tank is 1.2m deep, the surface rises at the rate of 0.012m/s. Calculate
the discharge of water flowing into the tank in m^3/s
a. 0.02 b. 0.05 c.0.08 d. 0.12

_______________6. Find the slope of the line whose parametric equations are x= 4t+6
and y= t-1.
a. -4 b. ¼ c. 4 d. -1/4

_______________7. Evaluate : lim (1-cosx)/x^2 , x approaching 0


a. 0 b.0.5 c.2 d.-0.5

_______________8.Arectangular box having a square base and open at the top is to have
capacity of 16823cc.Find the height of the box to use the least amount of material.
a. 16.14cm b. 32.28cm c. 18.341cm d. 28.74cm

_______________9.Find the area of the region bounded by the curves y= (12x/(x^2 +4),
the x-axis , and x=4
a. 4ln6 b. ln24 c.6ln15 d.6ln4

________________10. A solid is formed by revolving about the y-axis , the area


bounded by the curve y=x^4, the y-axis, and the line y=16.Find its centroid.
a.0,9.6 b.0,12.4 c.0,8.3 d.0,12.8

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