66 Problem 1: A student has written the following regarding an improper integral: " divergent because x + cos²x > x which implies divergent it follows that dx x + cos²x dx 1 x + cos²x X 1 < for all x > 0. Since we know X is is dx Jo is also divergent." x + cos²x (a) The student's conclusion is correct, but the argument is wrong. Can you find the flaw in the student's argument? (b) Find a correct comparison argument to show that the integral is divergent.

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