Find the volume of the solid obtained by revolving the curve
X = a cos3 θ , y = a sin 3 θ about the y-axis.
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Prove that
Find the intervals in R over which 
(t + 1)3 etdt is decreasing.
Prove that for every x > 0, x/1+ x2 tan -1 x < x.
Differentiate cos-1 (2x 2 -1) with respect to sin-1 squr(1 - x 2 ).
Find the maxima and minima, if any, for the function f given by
f (x) = x4 - 14x2 + 24x + 6.
Also find the values of the function at those points.
- 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)
Evaluate 