{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# test2-05 - Department of Mathematics University of Toronto...

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

Department of Mathematics, University of Toronto Term Test 2 – January 18, 2006 MAT 137Y, Calculus! Time Alloted: 1 hour 50 minutes Examiners: I. Alexandrova, M. Harada, V. Ivrii, G. Lynch, M. Saprykina, A. Savage 1. (10%) (a) Find a constant k for which lim x 0 sin x - x - kx 3 x 5 exists and the limit is also non-zero, and determine the value of the limit. (10%) (b) Find the equation of all tangent lines to the curve y = x 2 that intersect the point ( 1 4 , - 3 2 ) . (12%) 2. A poster is to have an area of 180 square inches with 1 inch margins at the bottom and sides and a 2 inch margin at the top. What dimensions will give the largest printed area? Make sure to verify that your answer yields a maximum. 3. Consider the function f ( x ) = x x 2 + 9 . (4%) (a) Show that f 00 ( x ) = 2 x ( x 2 - 27 ) ( x 2 + 9 ) 3 . (4%) (b) Find the domain, all intercepts, and asymptotes. (6%) (c) Locate all critical points of f , determine and clearly indicate the intervals for which f

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.

{[ snackBarMessage ]}

### Page1 / 2

test2-05 - Department of Mathematics University of Toronto...

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

View Full Document
Ask a homework question - tutors are online