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Unformatted text preview: / √ 3. 7. Let C be a curve given by a parametric equation ( x ( t ) ,y ( t )) where x (1) =2, y (1) = 4, x 00 (1) = 5, y 00 (1) =3. Find d 2 y dx 2 at t = 1. 8. Let f ( x ) = x 2 sin ± 1 x ¶ when x 6 = 0 and f (0) = 0. Show that f ( x ) exists for all x ∈ R but f ( x ) is not continuous. 9. Assume that f ( x ) is diﬀerentiable and that f ( x ) 6 = 0 for any x . (a) Find lim x → f ( (1 + 2 x ) 3 + 2 )f (1) f (1)f (tan( π/ 4x )) . (b) Given f (2) = 7, ﬁnd lim x → f (2 + 3 x )f (25 x ) 11 x . 10. Assume that f ( x ) is diﬀerentiable on [4 , 4], f (4) = 0 and f ( x ) is even. Show that f ( a ) = f ( a + 2) for some a ∈ [0 , 2]....
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This note was uploaded on 10/29/2010 for the course MATH 111 taught by Professor Ahmetguloglu during the Spring '10 term at Bilkent University.
 Spring '10
 AhmetGuloglu
 Calculus

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