Logarithms - Integration - Differentiate ... hence find problems.
Test Yourself 1.
Logarithms. | 1. (i) Differentiate y = (ln x)2.
(ii) Hence evaluate . Answer.Integral = 0.5. |
2. (i) If , show that
Answer.Integral = (ln3)/2. |
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3. (i) Show that .
(ii) Hence evaluate . Answer.Integral = 1. |
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4. Differentiate loge (loge x) and hence evaluate .
Answer.Integral = loge 2. |
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5. (i) Find the derivative of loge (x2 - 1).
(ii) Hence or otherwise find . Answer.Integral = 4loge (8/3). |
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6. Given that ,
evaluate giving your answer to 4 significant figures. Answer.Integral = 30.98. |
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7. Find the value of by first differentiating y = x loge x. Answer.Integral = 0. |
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8. (i) Find the derivative of (loge 6x)3 (ii) Hence evaluate . |
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9. (i) Show that (ii) Hence evaluate . |
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10. (i) Differentiate ex + e-x
(ii) Hence find . |
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