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What do the level curves look like? Prove that the rule for the surface of revolution thus obtained is z= f(√x2 + y2). Use this result to deduce that the equation x2+ y2+ 2x + 2y - z2+ 2 = 0 d
Sketch the curves given by the following parametric equations (find corresponding Cartesian equations if possible). In R3, x = 0, y = 3-3t, z = 2t, t ?R. Mark the points corresponding to t = 0, 1, -1.
Use the Mean Value Theorem to prove that at least one of us exceeded the speed limit, 100 km/h, by at least 10 km/h.
The function f is defined by f(x) = |x -1|. Sketch its graph. Observe that there is no value c such that f(3)-f(0) = f'(c)(3-0). Why does this not contradict the Mean Value Theorem?
Prove that if f is differentiable at a and f(a) 6= 0, then |f| is also differentiable at a. Give an example to show why the assumption f(a) 6= 0 is necessary.
Show that if f is continuous on the closed interval [a, b], then there is a function g which is continuous on R, and which satisfies g(x) = f(x) for all x in [a, b].
A mountaineer leaves home at 7am and walks to the top of the mountain, arriving at 7pm. Use the IVT to show that there is a point on the path that he will cross at exactly the same time of day on bo
Z is countable, because you can list all the integers in the order 0, 1,-1, 2,-2, 3,-3, ···. Is the set Q of all rational numbers countable? How about R and C?
Sketch and describe the following sets and their images under the function z → z2. The set of all points of the form z = x + 2xi.
Let r be a real constant greater than 2. The set {z ? C| |z + 1| + |z -1| = r} is a curve in the plane. Describe it and then find its equation in terms of x and y.
If the complex number z is imagined as a point in the complex plane. What are the complex numbers obtained from z by the following geometric transformations?
Using your answers to the previous part, find the following, expressing your answers first in polar then Cartesian (standard) form.
Find all solutions of the equation z2+ 3 + 4i = 0 by setting z = a + bi for some real numbers a and b. Solve z2+ z + 1 + i = 0.
The diameter of a car tire is 40cm and the diameter of a toy car tire is 18mm. Find the ratio of the diameter of the car to the diameter of the toy car.
Marvin currently has a balance of $1,192 in an account he has held for 14 years. He opened the account with an initial deposit of $800. What is the simple interest on the account?
J and B like a doughnut while they work on a week long stakeout. J ate 12 jam doughnuts and B ate 28. What percentage of all the doughnuts eaten did B account for?
An archaeological sample has only 25% of C-14 as much as in a living sample. Knowing that the half-life of C-14 is 5800 years, calculate the age of the sample.
Bob ate 10 carrots and 7 hershey kisees and the total calories were 263. fred ate 4 carrots and 8 hershey kisses and the total calories were 230. How many calories are in a carrot and a Hershey k
Create a quadratic equation, so that each of its roots will be 1 more than the corresponding root of the given quadratic equation.
How many more papers does Scott need to deliver? b) Scott continues to deliver papers at the same rate, How long will it take to deliver all of them?
Out of 180 students taking freshman composition, 70 own a car and 115 live on campus. If 10 students neither own a car nor live on campus, how many students both own a car and live on campus.
In a jar of red a green gumdrops, 12 more than half are red and the number of green gumdrops is 19 more than half the number of red gumdrops. How many of each are in the jar?
Combined out-of-pocket expenses for one person in poor health and one person in good health were $6213. Find the out-of-pocket expenses for each type of person.
After the delivery, what will the hieght of the fuel in the storage tank be, to the nearest tenth of a foot, if the storage tank had 1 foot of fuel in it before the truck unloaded its fuel?
Due to increased mailing costs, the new rate will cost publishers $36 million; this is 13.5% more than they paid the previous year. How much did it cost publishers last year?