1. Determine the following and simplify if possible. +fix cosh 2 X 1.1 sink 2x e sin. x 1.2 y = by using logarithmic differentiation. + x2 1.3 x3y + xy2= x 2. A particle moves along the path y = x...

1. Determine the following and simplify if possible. +fix
cosh 2 X 1.1 sink 2x
e sin. x 1.2 y = by using logarithmic differentiation. + x2 1.3 x3y + xy2= x 2. A particle moves along the path y = x –0,5x2 such that dx— =10 . dt
Find the value of when x = 5. dt
x\ 2z 2z 3. If z = arctan , show that —ax2+ = O.
d2 y 4. If y = cost and x = e2( sin 2t find —dx2 at t =0 5. The heat generated in a resistance weld is given by H =1d2Rt,where k is a constant, I is the current between the electrodes and t is the time for which current flows. H must not vary with more than 5% if the weld is to remain good. It is possible to control t to within 0,5% and R to within 2,4%. Estimate the maximum possible variation in current, I, if the weld is to retain its quality. (7) 6. Write down the first non-zero term in the Maclaurin series expansion of f (x) = .en sec x. (4) TOTAL: 40
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