Calculus  Integration  Reverse Chain Rule  Multifunction expressions.
Test Yourself 1  Solutions.
Exponential and log functions.  1.  2. . 
3.  4. 

5.  6.  
7. (i) log_{e} x = log_{e} 4 ∴ x = 4
(ii) 
(iii) If the area below the shaded region had been calculated, the statement for area would have been written as . We note there is a rectangle starting at the origin, extending vertically The rectangle consists of two areas  ∴ Area_{reqd} = Area_{rect}  Area_{(ii)} 

8. (i)
(ii)The two functions y = log_{e} x and touch at the point (e, 1) because the latter is a tangent. The graph shows that the log curve is below the tangent for all other values of x. 
(iii) 

Exponential and trig functions.  9. 
10. 
11.  12.  
13.  14. 

Log and trig functions.  15.  16. (i) (ii) 
17. (i) (ii) 
(iii) (iv) 

18.  
19.  20. 