Show that , the lagrange's form of remainder in the Maclaurin series expansion of e4x, tends to zero as
. Hence obtain the Maclaurin's infinite expansion for e4x.
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Verify the second mean value theorem for the function and
in the interval
.
Show that , the lagrange's form of remainder in the Maclaurin series expansion of e4x, tends to zero as
. Hence obtain the Maclaurin's infinite expansion for e4x.
Find a and b such that exists.
Determine the local minimum and local maximum values of the function f defined by .
Show that the function defined by
has an inverse by applying the inverse function theorem. Find its inverse also.
Check whether the set of integers is countable or not.
a) Test the following series for convergence,
(i)
(ii)
b) Show that is conditionally convergent.