Calculus - Integration - Reverse Chain Rule - Multi-function expressions.
Test Yourself 1 - Solutions.
Exponential and log functions. | 1. | 2. . |
3. | 4. |
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5. | 6. | |
7. (i) loge x = loge 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 - ∴ Areareqd = Arearect - Area(ii) |
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8. (i)
(ii)The two functions y = loge 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) |
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Exponential and trig functions. | 9. |
10. |
11. | 12. | |
13. | 14. |
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Log and trig functions. | 15. | 16. (i) (ii) |
17. (i) (ii) |
(iii) (iv) |
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18. | ||
19. | 20. |