Hi,
Why can't i use L'Hopital's rule in this limit:
lim (2x+sin2x+1)/(2x+sin2x)(sinx+3)^2 as x->infinity
Thanks...
I assume this is
$\displaystyle \lim_{x \to \infty}\frac{2x + \sin{2x} + 1}{(2x + \sin{2x})(\sin{x} + 3)^2}$.
You can only use L'Hospital's Rule if you get $\displaystyle \frac{0}{0}$ or $\displaystyle \frac{\infty}{\infty}$ from direct substitution.
But in this case, you'll get $\displaystyle \frac{1}{0}$.
Dear Prove It,
But notice that,
$\displaystyle \lim_{x\rightarrow{\infty}}\frac{2x+\sin{2x}+1}{(2 x+\sin{2x})(\sin{x}+3)^2}$
Dividing the numerator and denominator by "2x";
$\displaystyle \lim_{x\rightarrow{\infty}}\frac{1+\frac{\sin{2x}} {2x}+\frac{1}{2x}}{(1+\frac{\sin{2x}}{2x})(sinx+3) ^2}$
Therefore the limit does not exist.