Math 125 Quiz 1
Explain in your own words what is meant by the equation
lim
x
2f(x) = 5
Is it possible for this statement to be true and yet f(2) = 3? Explain.
Math 125 Quiz 2
Evaluate, if it exists,
lim
x
2
x2+x−6
x−2
Show your work!
Math 125 Quiz 3
The fuel consumption (measured in gallons per hour) of a car traveling at a speed of v
miles per hour is c=f(v).
(a) What is the meaning of the derivative f
(v)? What are the units?
(b) Write a sentence (in laymans’s terms) that explains the meaning of the equation
f
(20) = −0.05.
Math 125 Quiz 4
A manufacturer produces bolts of fabric with a fixed width. The quantity qof the fabric
(measured in yards) that is sold is a function of the selling price p(in dollars per yard), so
we can write q=f(p). Then the total revenue earned with selling price pis R(p) = pf(p).
(a) What does it mean to say that f(20) = 10,000 and f
(20) = −350?
(b) Assuming the values in part (a), find R
(20) and interpret your answer.
Math 125 Quiz 5
(a) The curve y=|x|/2−x2is called a bullet-nose curve. Find an equation for the
tangent line to this curve at the point (1, 1).
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen
(and show me what you get on this paper).
Math 125 Quiz 6
The equation x2−xy +y2= 3 represents a “rotated ellipse,” that is, an ellipse whose axes
are not parallel to the coordinate axes. Find the points at which this ellipse crosses the
x-axis and show that the tangent lines at these points are parallel.
Math 125 Quiz 7
A plane flying with a constant speed of 300 km/h passes over a radar station at an altitude
of 1 km and climbs at an angle of 30
. At what rate is the distance from the plane to the
radar station increasing a minute later?
Math 125 Quiz 8
The illumination of an object is directly proportional to the strength of the source and
inversely proportional to the square of the distance from the source. If two light sources,
one three times as strong as the other, are placed 10 ft apart, where should an object be
placed on the line between the sources to receive the least illumination?
