MATH 3B Midterm: Math 3B Exam 9
Document Summary
Try to answer the following questions without the use of book, notes or calculator. Time yourself and try to nish the test in less than 3 hours: gabriel"s horn is a mathematical object taken by rotating the curve y = 1 x around the x-axis for 1 x < . It can be shown (though not by what we have done) that the resulting surface of the horn has in nite area, i. e. , it is impossible to paint the outside of the horn. Find the volume of gabriel"s horn (i. e. , nd how much paint it would take to ll the inside of the horn): reduce the following to a single integral of the form az c. B stants a, b, c. f (x) dx for some con- 0 ( sin x + cos x)2 sin x dx: taylor series can be de ned for multivariable functions.
