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Unformatted text preview: x → 4, x <4, so x + 4 < 0. lim x →4 x + 4  x + 4 = lim x →4( x + 4) x + 4 = lim x →41 =1 5. *Prove that lim x → 2 1 x = 1 2 . Solution: 6. *If the function f is deﬁned by ± if x is rational 1 if x is irrational prove that lim x → f ( x ) does not exist. Solution: 7. Suppose that lim x → a f ( x ) = ∞ and lim x → a g ( x ) = c , where c is a real number. Prove each statement. (a) lim x → a [ f ( x ) + g ( x )] = ∞ (b) lim x → a [ f ( x ) g ( x )] = ∞ if c > (c) lim x → a [ f ( x ) g ( x )] =∞ if c < Solution: 8. From the graph of g, state the intervals on which g is continuous. Figure 1: Graph Solution: 9. Use the Intermediate Value Theorem to prove that there is a positive number c such that c 2 = 0. (This proves existence of the number √ 2) Solution: 2...
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 Spring '10
 Tor
 Calculus, Geometry, Equations, lim, Continuous function, x2 x2 lim

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