Algebra Answers

Which of the following statements are true? Give reasons for you answer. (This means that if you
think a statement is false, give a short proof or an example that shows it is false. If it is true, give a
short proof for saying so. For instance, to show that {1, Padma, blue} is a set’ is true, you need to
say that this is true because it is well defined collection of 3 objectives.)
(i) The domain of the function f given by
}. {1 \ R is
1 x
2 x
f(x)
2
2



(ii) Any curve with portions in the first and second quadrants is symmetric about y-axis.
(iii)
1
2
1
lim
1
lim
    x x x
does not exist.
(iv) An ever function cannot be monotonic.
(v) The curve
) 1 (
1
) 4 (
2
2

 
x
y
has no asymptote parallel to axes.
(vi) A function f, defined by f(x) = x sin x + cos x, is decreasing in
  . π/2 o,
(vii) If



1
1
, ) ( o dx x f
then f must be an even function.
(viii)
. cos cos sin
2 2
x x dt t
dx
d
x
x
 







(ix)
1 x 2 f(x) by given : f    R R
is differentiable on R.
(x) The