1Afinal2005

# 1Afinal2005 - Math 1A Final 2005-12-15 5:00-8:00pm You are...

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Math 1A Final 2005-12-15 5:00-8:00pm You are allowed 1 sheet of notes. Calculators are not allowed. Each question is worth 3 marks, which will only be given for a clear and correct answer in simpliﬁed form. 1. Draw the graph of the function y = | cos( x ) | for - π x π . 2. Evaluate the limit lim x 9 x 2 - 81 x - 3 . 3. Prove that x 4 + 1 = 3 x has at least one real root. 4. Diﬀerentiate e x / ( x + 1). 5. Find the derivative of the function y = cos(cos(cos( x ))). 6. Find dy/dx if x 2 y + xy 2 = 2 x . 7. Find the derivative D 57 sin(2 x ). ( D means d/dx ) 8. If f (1) = 10 and f 0 ( x ) ≥ - 1 for all x , what is the smallest possible value of f (5)? 9. Find lim x + x 1 /x . 10. Sketch the curve y = x ln( x ) 2 for x > 0. 11. Find two numbers whose diﬀerence is 10 and whose product is a minimum. 12. Use one iteration of Newton’s method applied to the initial approximation x 1 = 2 to estimate 9 1 / 3 . 13. Find a function
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## This note was uploaded on 08/03/2010 for the course ECONOMETRI 05 taught by Professor Wood during the Spring '10 term at Berkeley.

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