Write the inequality in the modulus form.
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Find a and b such that exists.
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.
a) If the partition P2 is a refinement of the partition P1 of [a,b], then and
. Verify this result for the function
defined over the interval
and the partitions
and
.
b) Evaluate: .
Write the inequality in the modulus form.
Check whether the intervals ]5,9] and [6,12[ are equivalent or not.
a) Determine the points of discontinuity of the function f and the nature of discontinuity at each of those points:
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Also check whether the function f is derivable at x = 1.
Using the principle of mathematical induction, show that