Answer to Question #67004 in Real Analysis for koel

Question

2.
(c)
(d)
(e)
(a)
The greatest integer
R is derivable in
lim cot x does
function
the interval
not exist.
(7c
of Mathematical
is convergent.
[-1
2 4
[x] defined on
Induction,
It It
-> - X --
2 2
The series
nZ
Using the Principle
show that
1 + 3 + 5 + 7 + + (2n - 1) = n2, V n E N.
(b) Show that the function f : [0, 1] -4 R
defined by
11 when x is rational
f(x) =
is not Riemann integrable. 4
(c) Show that the function
f(x) = I x - 5 I + x2 + 3x + 10
is continuous but is not differentiable at the
point x = 5