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Unformatted text preview: ath 125A Practice Exam 2 Page 6 of 8 7. ( pts ) Use the deﬁnition of the derivative to prove the Quotient Rule. 8. ( pts ) Use the deﬁnition of the derivative to show f (x) = x + x + 1 is not diﬀerentiable at
x = −1. Math 125A Practice Exam 2 Page 7 of 8 nx
for x ∈ [0, 1]. Let f (x) = 0 for
9. ( pts ) Let the sequence of functions {fn } be fn (x) =
1 + n2 x2
x ∈ [0, 1]. Prove {fn } does not converge uniformly to f on x ∈ [0, 1]. Math 125A Practice Exam 2 Page 8 of 8 The following extra credit problem is OPTIONAL and you are advised to ﬁnish the rest of the test
before trying this problem.
1. ( pts ) Prove that for all x0 ∈ R there exists a sequence of rational numbers which converges
to x0 . Also, there exists a sequence of irrational numbers which converges to x0 ....
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 Winter '07
 Fukuda
 Calculus, Power Series

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