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Unformatted text preview: lim x → 1 x 31 x 21 . 1 5. Let f ( x ) = 3 + 1 /x . In the deﬁnition of the limit lim x →∞ f ( x ) = 3, if ε = 1 / 5, how large must N be to guarantee that  f ( x )3  < ε for all x > N ? 6. Show that the equation x 4x1 = 0 has at least one real solution in the interval (1 , 2). 7. Diﬀerentiate the function f ( x ) = 2 x + 1 x + 3 . 8. Diﬀerentiate the function f ( x ) = √ x e x . 9. Find the values of x where the graph of y = x 36 x 2 has a horizontal tangent line. 2...
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 Fall '08
 WILKENING
 Calculus, Continuous function, infinite limit, Calculus Prof. Haiman, Prof. Haiman

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