101f04fin - B U Department of Mathematics Math 101 Calculus...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: B U Department of Mathematics Math 101 Calculus I Fall 2004 Final Calculus archive is a property of Bo˘gazi¸ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1.) Let f ( x ) =    √- x if x < 3- x if 0 ≤ x < 3 ( x- 3) 2 if x > 3 Determine the point(s) at which f ( x ) is discontinuous. Explain in detail. Solution: Check the points x = 0 and x = 3 because these are candidate points of discontinuity. x = 0 : lim x →- f ( x ) = lim x →- √- x = 0 lim x → + f ( x ) = lim x → + (3- x ) = 3 ⇒ lim x → f ( x ) doesn’t exist and therefore f is discontinuous at x = 0. x = 3 : lim x → 3- f ( x ) = lim x → 3- (3- x ) = 0 lim x → 3 + f ( x ) = lim x → 3 + ( x- 3) 2 = 0 ⇒ lim x → 3 f ( x ) = 0 but f (3) is undefined and therefore f is discontinuous at x = 3, too because for continuity we must have lim x → a f ( x ) = f ( a ) . 2.) For what values of r does the function y = e rx satisfy the equation y 00 + 5 y- 6 y = 0?...
View Full Document

This note was uploaded on 11/16/2011 for the course MATH 102 taught by Professor Soysal during the Winter '09 term at Boğaziçi University.

Page1 / 6

101f04fin - B U Department of Mathematics Math 101 Calculus...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online