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a) Show that d/dx(arcsin x) = 1/(√ (1-x²)). b) Hence, use a suitable trigonometric substitution to find ∫ (1/(√ (4-2x-x²))) dx.
Will be easier to explain with whiteboard!a) Let y = arcsin x. sin y = x cos y dy/dx = 1 dy/dx = 1/(cos y) dy/dx = 1/(√ (1 - sin 2 y)) dy/dx = 1/(√( 1 - x 2 )) as required.b) 4 - 2x - x 2 = - (x 2 + 2x - 4) ...
ED
Answered by
Emma D.
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Further Mathematics tutor
3248 Views
What best explains the collapse of royal authority in France by 1789?
What best explains the collapse of royal authority in France by 1789? Louis XVI was in theory an absolute monarch who ruled according to the Divine Right of Kings. However, by 1789 this theoretical power had...
GM
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Grace M.
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History tutor
7655 Views
What is the de Broglie wavelength? Why do we care?
The de Broglie wavelength is an important idea in physics that shows that all matter with mass can also show wave-like properties. For example, an electron (which we usually think of as a particle) can diffr...
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Answered by
Yorick E.
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Physics tutor
4953 Views
How do I structure an essay to get top marks?
There is a simple structure that is infallible. It starts with having a general structure, Introduction, Main body (with 3 main arguments), and Conclusion.The intro and conclusion have to be pre prepared, an...
AG
Answered by
Anna G.
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French tutor
2130 Views
How should I approach an unseen poem in an exam, such as Thomas Hardy's 'The Voice'?
Working through unseen poetry can be a really creative and thought-provoking process. I would advise the student to take a deep breath, shut out the context of the exam hall, and read the poem through slowly...
ZK
Answered by
Zara K.
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English Literature tutor
4237 Views
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