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Q7. (a) The blade efficiency E of a particular turbine is given by:

E = (2u(V-u)/V² )        Where u = the speed of the blade

V = the constant velocity of the jet.

Determine EACH of the following:

(i) the value of u for maximum efficiency; (6)

(ii) the maximum percentage efficiency. (2)

(b) Differentiate EACH of the following functions:

(i) 3/x³ -4/x² +2/√x-√x (4)

(ii) 2sin t – cos t – t + ln t. (4)