Practice Midterm 2 Solutions

Practice Midterm 2 Solutions - Math 125A 1 pts Let f(x =...

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Math 125A Practice Exam 2 Page 2 of 8 1. ( pts )Let f ( x )=s in 1 x . Use the defnition oF the limit to prove that lim x 0 f ( x )doesnotex ist . 2. ( pts ) ±ind the interval oF convergence For the Following power series ° 2 n n 5 n +1 x n
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Math 125A Practice Exam 2 Page 3 of 8 3. ( pts )Letthesequenceo ffunct ions { f n } be f n ( x )= x x n for x [0 , 1]. (a) Find f ( x )suchthat { f n }→ f on [0 , 1]. (b) Using the de±nition, prove { f n } does not converge uniformly to f (found in part a) on [0 , 1].
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Math 125A Practice Exam 2 Page 4 of 8 4. ( pts )Letthesequenceo ffunct ions { f n } be f n ( x )= 1 1+ nx for x [2 , ). Let f ( x )=0for x [2 , ). Using the deFnition, prove { f n } converges uniformly to f on x [2 , ).
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Math 125A Practice Exam 2 Page 5 of 8 5. ( pts )For x [0 , 1], we have the following power series 1+ x = ° ( 1) n (2 n )! (1 2 n )( n !) 2 (4 n ) x n . Use this fact to build a power series for 1 1 x 2 6. ( pts )Provethefo l low ingser iesconvergesun i form lyon R to a continuous function ° n =1 1 n 2 cos nx
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Math 125A Practice Exam 2 Page 6 of 8 7. ( pts ) Use the defnition oF the derivative to prove the Quotient Rule.
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Practice Midterm 2 Solutions - Math 125A 1 pts Let f(x =...

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