Trigo-limit

**dhiab** · November 12th 2009, 11:27 AM

Calculate :

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

**pickslides** · November 12th 2009, 12:07 PM

Originally Posted by dhiab

Calculate :

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

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

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

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

Now consider

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

does this help?

**DeMath** · November 12th 2009, 12:13 PM

Originally Posted by dhiab

Calculate :

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

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

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

$= 9\mathop {\lim }\limits_{x \to 0} \cos x + \mathop {\lim }\limits_{x \to 0} \cos x \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}<br /> {x} =$

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