**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 π/ 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) ﬁnd I 4 and I 5 ....

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- Spring '07
- BERMAN
- Math, Exponential Function, Inverse trigonometric functions, Complex logarithm, dx xa ln