Exercise 1.13 [Section 1, BOMC-2011]

[sourav das]

Sorry for my typing mistake.
I edited it now.
I'm very bad in typing....

[sourav das]

Both of the problems uses tricks which are taught in our high school, but that doesn't mean that they are negligible. On the other hand , it is a good thing that you learned and can use those right!

I agree with Mahi

[*Mahi*]

Sorry for my typing mistake.
I edited it now.
I'm very bad in typing....

Nope, it wasn't your typing mistake. Notice that $x=0$ makes the LHS of the given inequality undefined.

[sourav das]

No, I'm not saying for $x=0$
I'm saying it for writing "missing the part $x \leq -\frac{1}{2}$ "instead of "missing the part $x\geq -\frac{1}{2}$"
But i've edited that part...

[Jini]

In THIS case, this might actually have a value, you know $\frac{0}{0}$, which is smaller than $\frac{45}{8}$... Like $\frac{sinx}{x}$ tends to one as $x$ tends to zero...

[*Mahi*]

There might be, but we don't actually care about values like $\frac 0 0$s in inequality, and they are left out all the times. I mean, we includes $x \rightarrow 0$ as we have given the limit, but $x=0$ has no meaning, like $\frac {\sin x} x$ has no meaning when $x=0$.

[Jini]

Hmmm... Okay...

I have a knack for forgetting to review a problem for further details, very often causing me to make (devastating) silly mistakes. I guess I should try to be more cautious from now on