Math Ext 1 help (1 Viewer)

5uckerberg

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Q20
given that .
That means when









Note that which is in the form . Subbing it in we can see that it should be


Q21)






When . Thus,









Chuck the LHS in the calculator and you will see that

Q19) Show that
To start off lets split into which is just
Now, and we multiply both the numberator and demnoominator by giving us .
Rationalise the denominator it will give us as required.

Part ii
Complete the square on the denominator which in turn will give you and to find the area it is in the form of

Knowing this we will now have .
Let
When and when we have
Once we get here you should recognise that you have to find the inverse of tan which is is that just as discussed from part 1.

There,
Then integrate once again and this gives us .

Q25

i)


We are told initially the displacement is 1 cm so to interpret that we will say when and using that .



ii)

.
when , where n is an integer.
.
When .
When .
Maximum displacement is at intervals of "/>"/>
 
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