2000test2 - , 3], and has values f (1 . 0) = 0 . 1860, f (1...

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

View Full Document Right Arrow Icon
UNIVERSITY OF TORONTO AT SCARBOROUGH PHYSICAL SCIENCES DIVISION, Mathematics MATA26Y February 7, 2001 Term Test II [14] 1. Sketch the graph of the function f ( x ) = x 4   2 x 2 , showing extrema, points of inflection, intervals of increase and decrease and intervals of concavity. 2. Calculate the following. [4] (a) lim x →∞ x ± 2 1 x   1 ² [4] (b) lim x 1 p x 2 + x + 1   3 x [6] (c) lim x 0 x cos x   sin x x sin 2 x [6] (d) d dx ± (ln x ) arctan x ² [12] 3. Find the length of the shortest ladder that can extend from a vertical wall, over a verti- cal fence p 3 m high located 9 m away from the wall, to a point on the ground outside the fence. b b b b b b b b b b b b b b ± ± ² ² ² 3 9 m wall ladder fence y x [4] 4. (a) State the Fundamental Theorem of Calculus. [8] (b) Find the area bounded by f ( x ) = 4   x 2 and the x –axis on [   4 , 4]. [4] (c) Find f 0 ( x ) where f ( x ) = Z 1+ x 2 sin x e t 2 dt . [8] 5. A function f satisfies j f (4) ( x ) j 7 on the interval [1
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.

Unformatted text preview: , 3], and has values f (1 . 0) = 0 . 1860, f (1 . 5) = 0 . 9411, f (2 . 0) = 1 . 1550, f (2 . 5) = 1 . 4511, and f (3 . 0) = 1 . 2144. Find the best possible Simpsons rule approximation to I = R 3 1 f ( x ) dx , based on this data. Give a bound for the size of the error, and specify the smallest interval you can that must contain the value of I . MATA26Y page 2 6. Calculate each of the following integrals. [4] (a) I = Z cos 1 2 d [4] (b) I = Z xe x dx [4] (c) I = Z p 1 2 x dx [4] (d) I = Z dx x 2 4 7. Calculate each of the following integrals. [4] (a) I = Z 3 2 x p 1 x 2 dx [6] (b) I = Z 3 2 p 1 x 2 dx [4] (c) I = Z e x sin xdx...
View Full Document

Page1 / 2

2000test2 - , 3], and has values f (1 . 0) = 0 . 1860, f (1...

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