Q20
dy=\frac{dx}{\sqrt{2-x^{2}}})
given that
=0)
.
That means when
}})
Note that
=0)
which is in the form
=...)
. Subbing it in we can see that it should be
Q21)
}=0.1t+D)
When

. Thus,

Chuck the LHS in the calculator and you will see that
Q19) Show that
= \sqrt{3}+2)
To start off lets split
)
into
)
which is just
)
Now,
\right)=\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}=\frac{\frac{1}{\sqrt{3}}+1}{1-\frac{1}{\sqrt{3}}})
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
^{2}+4)
and to find the area it is in the form of
Knowing this we will now have
^{2}+4}dx)
.
Let

When

and when

we have

Once we get here you should recognise that you have to find the inverse of tan which is
=\theta)
is that just

as discussed from part 1.
There,
^{2}+4}dx=\int_{-\frac{\pi}{4}}^{\frac{5\pi}{12}}d\theta)
Then integrate once again

and this gives us

.
Q25
i)
=-\cos{t}+C)
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.
e^{1-\cos{t}})
.
When

.
When

.
Maximum displacement is

at intervals of
\pi[TEX] where n is a natural number.)
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