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.
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Give an example, with justification, of a periodic function which is not even.
Find the volume of the solid obtained by revolving the curve
X = a cos3 θ , y = a sin 3 θ about the y-axis.
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.
Prove that
Trace the curve x = a (θ - sin θ ), y = a (1 - cos θ ). State the properties you use for tracing it, also.
- hich of the following statements are true or false? Give reasons for your answers.
- The greatest integer function is continuous on R .
- The domain of the function f , given by
iii) The function f , defined by f (x) = x 3 - 6x 2 + 16x - 15, is increasing in R .
iv) Rolle’s theorem is applicable for the function f , defined by
f (x) = 1 + x 2 /3 in the interval [-1,1].v)
Find the length of the curve y = In 
from x = 1 to x = 2