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Exam 1 Review - TA

# Exam 1 Review - TA - Extra Review Problems Here are the...

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Extra Review Problems Here are the problems I brought to the review session. My suggestion is to prioritize understanding previous homework problems over attempting these new problems. I apologize for any typos which may exist. Feel free to email me about any problem for a hint ([email protected]). Some problems may be more challenging or more ambiguous than what you would see on an actual exam. Good luck on Monday! Inequalities: 1. Give a simple description of { ( x,y ) R : x 2 + xy + y 2 0 } Answer: R 2 2. For a > 0, prove the minimum of ax 2 + bx + c is attained at x = - b 2 a . Hint: The inequality you are trying to show is: ax 2 + bx + c a ( - b 2 a ) 2 + b ( - b 2 a ) + c . Try getting all terms on one side and factoring. 3. Prove x,y R where y > 0, we have x 2 + y 2 x y Hint: Make a wise substitution into the AGM inequality 4. Prove x,y 0, x +4 y 4 xy Hint: Make a wise substitution into the AGM inequality 5. A circle is deﬁned by x 2 + y 2 + ax + by = c . Show why we need c ≥ -

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Exam 1 Review - TA - Extra Review Problems Here are the...

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