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Material Type: Exam; Professor: Rosenthal; Class: UNIVERSITY CALCULUS II; Subject: MATHEMATICS; University: St. John's University-New York; Term: Spring 2009;
Typology: Exams
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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.
(b) Differentiate y = cosh(x^3 − 1).
(c) Prove that the function y = f (x) = C cosh 5x + D sinh 5x, where C and D are constants, is a solution of the differential equation y′′^ − 25 y = 0.
(d) Evaluate
cosh x − sinh x dx.
2 MTH 1740: PRACTICE TEST 2
2 45 until it hits the ground, where y is its height above the ground and x is the horizontal distance traveled in meters. Set up, but do not evaluate, an integral that will calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground.
Bonus Using the Principle of Mathematical Induction, prove that 2n+3^ ≤ (n + 3)! for all integers n ≥ 1.