Give an example of a function which is one to one but not onto, with reason.
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Evaluate 
Trace the curve x = a (θ - sin θ ), y = a (1 - cos θ ). State the properties you use for tracing it, also.
Prove that 
Find the domain of the function f, defined by f (x) = sqrt (x3 (9-x)).
For which value(s) of k, is the function f, defined as below, continuous at x = 2?
Further, at which other points in [1, ∞ [ is f continuous, and why?
The cost of fuel is running an engine is proportional to the square of the speed in km/h and is ` Rs 48 per hour when the speed is 16 km/h. Other costs amount to ` Rs300 per hour. Find the most economical speed.
Give an example, with justification, of a periodic function which is not even.