Marh%20119%202006-2007%20Fall%20MidTerm2

Marh%20119%202006-2007%20Fall%20MidTerm2 - Give graph of...

This preview shows pages 1–6. Sign up to view the full content.

Group List No. Last Name Name Student No. Department Section Signature : : : : : : : : : : : : : Code Acad. Year Semester Coordinator Date Time Duration M E T U Department of Mathematics CALCULUS I Mid Term 2 Math 119 2006-2007 Fall Muhiddin Uguz December.4.2006 09:30 136 minutes 9 QUESTIONS ON 6 PAGES TOTAL 60 POINTS 1 2 3 4 5 6 7 8 9 Show Your Work Question 1 (9 points) Let f ( x ) be the function f ( x ) = 1 5 x 5 + 1 3 x 3 + 2 x - 8 15 . a) Prove that f ( x ) is invertable. b) Find the ±rst derivative of the inverse of f at x = 2 , i.e. ±nd d dx ( f - 1 ( x ))(2). c) Find the second derivative of the inverse of f at x = 2 , i.e. ±nd d 2 dx 2 ( f - 1 ( x ))(2). Muhiddin UĞUZ

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

View Full Document
Question 2 (6 points) Find the area of the region bounded by the curves y = x 2 - 1 , y = 0 , x = - 1 and x = 2. Question 3 (6 points) Find the volume of the solid obtained by rotating the region bounded by the curves y = 2 x - x 2 and y = 0 about y -axis. Muhiddin UĞUZ
Question 4 (6 points) Let f ( x ) be diﬀerentiable function such that Z 0 g ( x ) f ( t ) dt = sin( g ( x )). It is also given that g (1) = π and g 0 (1) 6 = 0. Find f ( π ). Question 5 (6 points) Find all asymptotes of f ( x ) = x 3 + 2 x 2 + 2 x 2 - 1 . Muhiddin UĞUZ

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

View Full Document
Question 6 (6 points)

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Give graph of the derivative of f ( x ), that is y = f ( x ), answer the following questions about the function itself : a) Find the intervals on which f ( x ) is decreasing. b) Find the intervals on which f ( x ) is concave up. c) If f (0) = 0 compute f (119). Question 7 (6 points) Find lim n →∞ n X i =1 i 4 n 5 . Muhiddin UĞUZ Surname: . ................ Name: . ................. Id: . ................. Section: . ............... Question 8 (9 points) a) Evaluate Z 4 1 x 2 + 6 √ x dx b) Evaluate Z 6 e dx x ln( x ) c) If y = ( x 3 4 ) √ x 2 + 1 (3 x + 2) 5 , using logarithmic diﬀerentiation , Fnd dy dx . Muhiddin UĞUZ Question 9 (6 points) Find an equation of the line through the point (1 , 2) that cuts oﬀ the least area from the ±rst quadrant(i.e. where x ≥ , y ≥ 0). Prove your answer. Muhiddin UĞUZ...
View Full Document

This note was uploaded on 11/01/2011 for the course CHEMICAL E CHEM-107 taught by Professor Bilinmiyor during the Spring '11 term at Middle East Technical University.

Page1 / 6

Marh%20119%202006-2007%20Fall%20MidTerm2 - Give graph of...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online