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# Calculus :Tutorial 2

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### Calculus :Tutorial 2

1. 1. PMB 3004: Calculus Tutorial 21. Change the following improper rational functions to the proper rational functions: a) ( x3 + 5x2 – x – 6) / (x-1) b) (4x3 – 2x2 - x + 3 ) / x -2 c) (4x3 + 6x2 + 5x +3) / (2x-1) d) (x3 + 5x2 - 2x -1) / (x+3)2. Simplify the following expressions: a )2e3 3e 7 d) e2 x (e2 x  e x  1)  e x (1  e x ) e 1.5 b) e2 x  e x 5e1/ 2 e) x  1  ex e 4e3 3e 1 f) e2 x  (1  e x )2 c) 2 e 3 e 23. Simplify the following expressions: a ) ln x  2 ln x  3ln x e) 4log rs 2 t  2log r 2 st 2 1 b) ln t  ln t 1 x2 1 x3 2 f) log 2  log 6 2 y 3 y c) log a 100  log a 10  log a 5 10 ln x  ln x  ln x 3 d) ln x 9  ln x4. Solve the following equations:
2. 2. a) 25x  1253 h) log10 4 x 2  2b) x 5  32 i) 2ln(3t  5)  4 1c) 2 x 1  j) log x  log 2  1 16 k) 3ln(e3 x 4 )  9d) e ln 2 x  4e) e2 x  3e x l) 2log(x  2)  log(2x  5)f) 1 2 m) log(x 2  6)  log(x  1)  1 e 1 x n) eln x  2x  3g) 10 x 6  30 PMB/ NS/Jan 09