(a)
Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :
(b) The series
converges by comparison to the convergent <em>p</em>-series,
(c) The series
converges absolutely, since
That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.
The time taken by the object to fall from 15 m on the Mercury which has a gravity of 3.7 m/s² is 10.54 seconds.
<h3>What is kinematics?</h3>It is the study of the motion of a body without considering mass. And the reason behind them is neglected.
The object is on Mercury and starts falling from rest.
As it is on Mercury there is no air resistance to account for.
Gravity on Mercury is 3.7 m/s².
Then the time taken by the object to fall from 15 m will be given as
More about the kinematics link is given below.
#SPJ1
