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Maths and Vibrations Tutorial Sheet 4 Solutions

Mathematic

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Maths and Vibrations Tutorial Sheet 4 Solutions

i) 3



ii)

iii) 2

Review product, chain and quotient rules

i)

ii)

iii)

iv)

v)

vi)

vii)

(solution is easily found knowing hence differentiate with quotient rule)

i

Given we can see y=2 for x=0

we can find points where curve cuts x axis (y=0) by factorising

hence x=-1, x=2 for y=0.

So curve cuts the axes at (0,2) , (-1,0) and (2,0).

Turning point (i.e. stationary point) when , hence x=0.5 and y=2.25

Since turning point is a maxima.

4) Given , from chain rule

hence





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