Trigonometric functions - Calculus - Differentiate ... hence find.
Test Yourself 1.
The questions on this page all require you:
1. to differentiate the first equation/expression; and
2. to use the results of that differentiation to determine the integral of another.
1. (i) Differentiate x cosx.
(ii) Hence evaluate . Answer.I = 1. |
2. (i) Differentiate y = x2 + 1.
(ii) Hence find . |
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3. (i) Differentiate sinx - x cos x.
(ii) Hence find . Answer.I = 1. |
4. By differentiating y = cos x, find
. |
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5. | 6. | |
7. Use the trigonometry identity to show that |
8. (i) Differentiate y = x tan x. (ii) Hence find an expression for (also using the results of Q7). |
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9. (i) Differentiate
. (ii) Hence find . Answer.-3/4. |
10. (i) Differentiate cos2(3x) with respect to x.
(ii) Hence evaluate . Answer.(ii) Integral - 2. |
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11. | 12. | |
13. (i) Show that
tan3 x = tan x sec2 x - tanx (ii) Hence find |
14. | |
Applications | 15. (i) Differentiate sin (x2).
(ii) Use this result to find the exact area bounded by y = xcos (x2), the x axis and the lines x = 0 and x = 1. |
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16. (i) By expressing cot x as prove that .
(ii) Find the area of the region bounded by the curve y = cosec2 x, the x axis and the lines π/6 and x = π/3. |