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Unformatted text preview: √ 12 x x (d) lim t → t t + sin t 1 (e) lim z →∞ z 2 + 1 2 z 21 (f) lim x →∞ cos x x 2 + 1 2. Let f ( x ),∞ < x < ∞ , be the function deﬁned as follows: f ( x ) = ( x + λ if x ≤ 2 2 λx if x > 2 (a) Determine the constant λ so that f ( x ) is continuous for all x . (b) Graph the function y = f ( x ),4 ≤ x ≤ 8, for the value of λ found in (a). 2 3. Show that the function f ( t ) = cos tt has a zero in the interval π/ 6 < t < π/ 4. 4. Using only the deﬁnition of the derivative, ﬁnd f ( x ) for the following functions: (a) f ( x ) = 1 √ x 2 + 1 (b) f ( x ) = x 1 + 2 x 3...
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 Winter '06
 denissjerve
 Calculus, Derivative, Englishlanguage films, Continuous function, Homework help service

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