test2-0607 - Department of Mathematics, University of...

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

View Full Document Right Arrow Icon
Department of Mathematics, University of Toronto Term Test 2 – January 15, 2007 MAT 137Y, Calculus! Time Alloted: 1 hour 50 minutes 1. (9%) (i) Find the equation of the tangent line to the graph of y = sec x - 2cos x at the point ( π 3 , 1 ) . (9%) (ii) For the equation x 2 + 4 xy + y 3 + 5 = 0, find d 2 y dx 2 at the point ( 2 , - 1 ) . 2. (10%) (i) A balloon is rising at a constant speed of 5 3 meters per second. A boy is cycling along a straight road at a speed of 5 meters per second. When he passes under the balloon, it is 15 meters above him. How fast is the distance between the boy and the balloon changing three seconds later? (10%) (ii) Consider the function f ( x ) = ( x 2 sin 1 x , x 6 = 0 , 0 , x = 0 . . Prove that f is differentiable at 0, and find f 0 ( 0 ) . 3. Consider the function f ( x ) = x / ( x - 1 ) 2 . (5%) (a) Find the domain, the x - and y -intercepts, and asymptotes. (6%) (b) Given that f 0 ( x ) = - x - 1 ( x - 1 ) 3 , locate all critical points of f , determine and clearly indicate the intervals for which f is increasing or decreasing, and classify all critical points as
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/09/2010 for the course MAT 137 taught by Professor Uppal during the Spring '08 term at University of Toronto.

Page1 / 2

test2-0607 - Department of Mathematics, University of...

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