Unformatted text preview: a n = F n F n + 1 . 4. Consider the statement: lim x → a f ( x ) = L . (5%) (a) Give the formal ε , δ deﬁnition of the statement above. (10%) (b) Give a formal ε , δ proof that lim x → 3 x 2 + 7 x + 1 = 4. 5. (5%) (a) State the Intermediate Value Theorem. (10%) (b) Prove that there exists a nonzero solution to the equation sin x = x 2 . (10%) 6. Suppose we are given a function f such that for all values a , b ∈ R ,  f ( b )f ( a )  ≤  ba  . Prove that f must be continuous for all x . 1...
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This note was uploaded on 04/09/2010 for the course MAT 137 taught by Professor Uppal during the Spring '08 term at University of Toronto.
 Spring '08
 UPPAL
 Calculus, Limits

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