Find the intervals in R over which 
(t + 1)3 etdt is decreasing.
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Differentiate tan -1 [sin x - cos x /sin x + cos x]
with respect to 1/2 x.
Trace the curve x = a (θ - sin θ ), y = a (1 - cos θ ). State the properties you use for tracing it, also.
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she begins by running at a constant speed till she reaches a hilly portion 2 km from her home. Here her speed slows down while she runs up the hill, which is a 1-km run. Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance from her home. Also find the range of this function.
Trace the curve x(y2 + 4) = 8, stating all the points used for doing so.
Find the area enclosed by the curve r = a (1 - cos θ).
If y = emtan -1 x , show that (1 + x2 ) y n+1 (2nx - m) yn n(n -1)y n -1 = 0.
Prove that
