Calc Problem

**calc_help123** · December 24th 2008, 11:51 AM

The function f is defined by

f(x)=
(sinx)/(x) , x ≠ 0

1, x=0

A) at what points does its graph cross the x-axis?
B) What is the relation between x and tanx at points x≠0 at which f'(x)=0
C)What is the behavior of f as the absolute value of x approaches infinite

**galactus** · December 24th 2008, 12:22 PM

A: $\frac{sin(x)}{x}=0$

$x=C{\pi}$

B: $f'(x)=\frac{cos(x)}{x}-\frac{sin(x)}{x^{2}}$

$\frac{cos(x)}{x}=\frac{sin(x)}{x^{2}}$

$x^{2}cos(x)=xsin(x)$

$x=\frac{sin(x)}{cos(x)}=tan(x)$

C:

$\lim_{x\to {\infty}}\frac{sin|x|}{|x|}$

$\lim_{x\to {\infty}}\frac{sin(-x)}{-x}=\lim_{x\to {\infty}}\frac{-sin(x)}{-x}=\lim_{x\to {\infty}}\frac{sin(x)}{x}$

See the limit?.