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Q: Two light sources of identical strength are placed 10 m apart.

Two light sources of identical strength are placed 10 m apart. An object is to be placed at a point P on a line l parallel to the line joining the light sources and at a distance meter from it (see th...

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Q: The speeds of sound c1 in an upper layer and c2 in

The speeds of sound c1 in an upper layer and c2 in a lower layer of rock and the thickness h of the upper layer can be determined by seismic exploration if the speed of sound in the lower layer is gre...

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Q: Investigate the family of curves given by f (x) =

Investigate the family of curves given by f (x) = xne-x, where n is a positive integer. What features do these curves have in common? How do they differ from one another? In particular, what happens t...

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Q: Find the dimensions of a rectangle with area whose perimeter is as

Find the dimensions of a rectangle with area whose perimeter is as small as possible.

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Q: Ornithologists have determined that some species of birds tend to avoid flights

Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than ove...

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Q: (a). Graph the function. (b). Explain

(a). Graph the function. (b). Explain the shape of the graph by computing the limit as x→0 or as x→∞. (c). Estimate the maximum and minimum values and then use calculus to find the exact values. (d)....

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Q: (a). Graph the function. (b). Explain

(a). Graph the function. (b). Explain the shape of the graph by computing the limit as x→0 or as x→∞. (c). Estimate the maximum and minimum values and then use calculus to find the exact values. (d)....

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Q: (a). Graph the function. (b). Use

(a). Graph the function. (b). Use l’Hospital’s Rule to explain the behavior as x→0. (c). Estimate the minimum value and intervals of concavity. Then use calculus to find the exact values.

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Q: Find the maximum area of a rectangle that can be circumscribed about

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L and width W. [Hint: Express the area as a function of an angle θ.]

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Q: A steel pipe is being carried down a hallway 9 ft wide

A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carrie...

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