MTH 1740: PRACTICE TEST 2
University Calculus II
Spring 2009
Dr. Rosenthal
DISCLAIMER: This practice test is a guide to organizing your studies and an indication of the
difficulty of the test problems, as well as the amount of time required to finish the test. You are
absolutely responsible for all of the class notes and homework for the test. You may not conclude
that a certain topic is not on the coming test just because it is not on the practice test. You may
not conclude that a certain topic is on the coming test just because it is on the practice test.
1. (a) Simplify the expression: tanh(ln x).
(b) Differentiate y= cosh(x3−1).
(c) Prove that the function y=f(x) = Ccosh 5x+Dsinh 5x, where Cand Dare
constants, is a solution of the differential equation y00 −25y= 0.
(d) Evaluate Z1
cosh x−sinh xdx.
2. Sketch the polar equation r= 1 + 2 cos 2θ.
3. Find the distance between the points with polar coordinates (r, θ)=(−√2,7π
4) and
(r, θ) = (2,π
6).
4. Write down an integral that will calculate the area of one of the petals of the 8-petal
rose, r= sin 4θ.
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