problem_set_1 - Name Section Student ID Last First MI Math...

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1 Name: First MI Last Student ID # Math 32A Lecture #5 Fall 2007 Problem Set #1 Score Section: Problem # 1. For the general quadratic polynomial ax 2 + bx + c with a ≠ 0, derive the quadratic formula. I.e. that solutions to the equation ax 2 + bx + c = 0 (with b 2 ≥ 4ac) are given by x b b 2 4 ac 2 a . Hint: To get the idea, first treat the case a = 1; the object of the game is to “complete the square”. C REDIT 2 1 0 C REDIT 2 1 0 If f ( x ) e x , find f ( x ). Problem #2. (No derivation is required.)
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2 Problem Set #1 C REDIT 2 1 0 y e - x 2 x , find dy dx . (No derivation is required.) Problem #3. If C REDIT 2 1 0 Problem #4 . Let h ( t ) 1 e t . Find h ( t ). (No derivation is required.) C REDIT 2 1 0 Note: At UC LA , in this course, in this Lecture, the preferred notation for “natural logarithms” is simply an unadorned log; i.e. we will not adhere to the old–fashioned “ln”. Logarithms to other bases – which anyway rarely come up – will be denoted in the usual fashion e.g. log a ( x ).
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