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Q7) (a) The velocity, v, of waves of length, x, in a canal, may be determined from the formula v²=  gx/2π + 2πT/ρx

where T is the surface tension of the water and ρ is its density.

Determine EACH of the following:

(i) the value of x for minimum value of v²; (8)

(ii) the minimum value of v.   (4)

(b) Determine the first and second derivatives of the following function:

u = sin⁡ t-log_et (4)