Hey guys im new here, but I have a test today and I need to understand trig limits better.

lim of x approaching 0

sin(4x)

sin(6x)

the hint that was given was "use the identity Lim x approaching 0

sinx= 1"

x

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- Oct 8th 2008, 05:31 AMfortplainmantrigonometric limits
Hey guys im new here, but I have a test today and I need to understand trig limits better.

lim of x approaching 0

__sin(4x)__

sin(6x)

the hint that was given was "use the identity Lim x approaching 0

__sinx__= 1"

x - Oct 8th 2008, 05:35 AMfortplainman
oh and another question, which is on the def. of a derivitive, i just cannot remember the equation of a tangent line/equation of the normal line.

- Oct 8th 2008, 05:35 AMChop Suey
Multiply by $\displaystyle \frac{x}{x}$, so that you would get:

$\displaystyle \frac{\sin{4x}}{x} \cdot \frac{x}{\sin{3x}}$

What's left is simple manipulation to get your limit into something like sin(u)/u - Oct 8th 2008, 05:38 AMChop Suey
The derivative is the slope of the tangent line. The equation of a line in point slope form is given by:

$\displaystyle y - y_1 = m(x-x_1)$

Where $\displaystyle (x_1, y_1)$ is the point in question and m is the slope. The equation of the normal line to this line contains $\displaystyle (x_1, y_1)$, but its slope is the negative reciprocal of the original line.

For instance, if line K has a slope of 4, then the line that is perpendicular/normal to line k will have a slope of $\displaystyle -\frac{1}{4}$. Just remember that:

$\displaystyle m_{line} \cdot m_{normal} = -1$ - Oct 8th 2008, 05:40 AMfortplainman
oh ok I thought i was right on the tangent equation, but thanks for the normal info and hopefully the trig limit info will help me out. thanks.

- Oct 8th 2008, 05:46 AMfortplainman
- Oct 8th 2008, 06:46 AMPlato
$\displaystyle \frac{{\sin (4x)}}

{{\sin (6x)}} = \left( {\frac{4}

{6}} \right)\left( {\frac{{\frac{{\sin (4x)}}

{{4x}}}}

{{\frac{{\sin (6x)}}

{{6x}}}}} \right)$