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Graphs of rational functions and in particular asymptotes
In photography fixed focal length means that the focal length is not adjustable. Photographers are unable to zoom in and out on a particular subject when using such a lens. Not being able to easily zoom in on a subject might seem like a huge disadvantage. But such lenses are credited with being able to produce much higher quality pictures in controlled settings.
In order for a film camera with a fixed focal length F to focus on an object located a distance x from the lens, the film must be placed a distance y behind the lens. F, y, and x are related as follows
1/F = 1/X =1/Y
Now suppose a camera has a lens with focal length F = 65.
1. Explain what happens to the focusing distance y as the object moves far away from the lens.
2. Explain what happens to the focusing distance y as the object moves closer and closer to the lens.
3. In general, why can rational function cross a horizontal asymptote and why can it not cross a vertical asymptote?
If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per sec, then its height after t seconds is given by the equation h=-16t2+80t+96 where h is in feet. after how many seconds will the object reach a height ..
Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
LetR be the region bounded by the graph of f(x)=3x^2+6x and g(x)=18x-5x^2. Determine the area of R
Determine the amount of slack or surplus for each constraint
two car models are tested for a difference in average gas mileage. ten cars of model a averaged 32.1 miles per gallon
Verifying some important results over real valued functions - real-valued functions
Write an excel document that calculates the medication levels in the bloodstream for the first two weeks of taking this medication
A manufacturer has been selling lamps at $6 apiece, and at this price, consumers have been buying 3,000 lamps per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in price
Show that f is a homeomorphism. Isn't a homeomorphism by definition a bijection? And since M is compact, will it not be true that N will be compact too?
Plot the straight line developed from the Linear Trend equation, and the actual Peak demand versus the time, with time being the independent variable.
alishas three cats are on special diets. scout is the least active. sqeaky the most active is allowed triple the amount
Two fire towers are 30km apart, tower A being due west of tower B. A fire is spotted from the towers, and the bearings from A and b are E 14 N and W 34 N, respectively. Find the distance d of the fire from the line segment AB.
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