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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 - sin2y)) dy/dx = 1/(√( 1 - x2)) as required.b) 4 - 2x - x<...

Answered by Emma D. Further Mathematics tutor
1961 Views

What's the difference between diffusion and osmosis?

Osmosis is the net movement of water from an area of high water potential to low water potential through a semi-permeable membrane, while diffusion is the net movement of any liquid or gas from an area of...

Answered by Rosalind R. Biology tutor
9234 Views

Simplify: 5x + 8y - 3x + 9y

When you first come across algebra, it may be a bit tricky to get your head around as it involves more abstract concepts than we may have previously seen in maths. However, once you understand the basic p...

Answered by Katharine S. Maths tutor
3176 Views

Describe the course of blood through the heart and lungs, explaining how it becomes oxygenated.

Considering the heart has 4 distinct chambers - for this question it's best to start in the right atrium. (Supported by a diagram) Deoxygenated blood is returned to the right atrium from the rest of the b...

Answered by Liam R. Biology tutor
1727 Views

Complete and balance the equation: Mg(OH)2 + HCl -> ??

This relies on the knowledge that an acid + base --> salt + water.Once you have realised this - pick out the acid and the base (remember acids have H+ and bases OH-)Now, you know that water will be mad...

Answered by Sophie A. Chemistry tutor
3123 Views

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