This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (Simplify your answer but do not evaluate it numerically.) 4. (a) Prove or disprove: (i) tan-1 x = O (1) (ii) x-2 3 x grows slower than x 2 x (iii) log 2 3 x 2 grows at the same rate as ( x + 7) 2 (iv) 1 x = o 1 ln x (b) If f = O ( g ) and g = O ( h ) , is it true that f = O ( h ) ? Explain. 5. Evaluate the following integrals: (a) Z x e-x 2 dx (b) Z dx x-x 2 (c) Z x a ln x dx ( a =-1) (d) Z 2 x-1 x 2 + 2 x + 2 dx 6. For each integer n , let I n = Z / 4 tan n x dx . (a) Find I and I 1 . (b) Find a formula expressing I n +2 in terms of I n . (c) Deduce a formula expressing I n +4 in terms of I n . Hence (or otherwise) nd I 4 and I 5 ....
View Full Document
This test prep was uploaded on 02/15/2008 for the course MATH 1910 taught by Professor Berman during the Fall '07 term at Cornell University (Engineering School).
- Fall '07