1. ## Trigo-limit

Calculate :

LIM ( 9x + sin(x))/(x sec(x))
x---> 0

2. Originally Posted by dhiab
Calculate :

LIM ( 9x + sin(x))/(x sec(x))
x---> 0
$\displaystyle \lim_{x \to 0} \frac{9x+\sin(x)}{x\sec(x)}$

$\displaystyle \lim_{x \to 0} \left(\frac{9x}{x\sec(x)}+\frac{\sin(x)}{x\sec(x)} \right)$

$\displaystyle \lim_{x \to 0} \left(\frac{9}{\sec(x)}+\frac{\sin(x)}{x}\frac{1}{ \sec(x)}\right)$

Now consider

$\displaystyle \lim_{x \to 0} \frac{\sin(x)}{x}=1$

does this help?

3. Originally Posted by dhiab
Calculate :

LIM ( 9x + sin(x))/(x sec(x))
x---> 0
$\displaystyle \mathop {\lim }\limits_{x \to 0} \frac{{9x + \sin x}} {{x\sec x}} = \mathop {\lim }\limits_{x \to 0} \frac{{\cos x\left( {9x + \sin x} \right)}} {x} =$

$\displaystyle = \mathop {\lim }\limits_{x \to 0} \left( {9\cos x + \cos x \cdot \frac{{\sin x}}{x}} \right) =$

$\displaystyle = 9\mathop {\lim }\limits_{x \to 0} \cos x + \mathop {\lim }\limits_{x \to 0} \cos x \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}} {x} =$