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.
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Show that the function defined by
has an inverse by applying the inverse function theorem. Find its inverse also.
Find a and b such that exists.
Using the principle of mathematical induction, show that
Are the following statements true or false? Give reasons for your answer.
a) Complement of the open interval ]0, 1] is an open set.
b) Every bounded sequences is not convergent.
c) The function defined by
is uniformly continuous.
d) If the first derivative of a function at a point vanishes, then it has an extreme value at that point.
e) The function defined by
is not integrable.
Determine the local minimum and local maximum values of the function f defined by .
Find the following limit
Prove that a strictly decreasing function is always one-one.