- #1
VinnyCee
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Homework Statement
Find the tangent line equation for y = sin x at x = [itex]6\,\pi[/itex].
Homework Equations
[itex]m_{tangent}\,=\,\lim_{h \to 0}\,\frac{f(c+h)\,-\,F(c)}{h}[/itex]
[itex]y\,-\,y_1\,=\,m\,(x\,-\,x_1)[/itex]
The Attempt at a Solution
[itex]m_{tangent}\,=\,\lim_{h \to 0}\,\frac{f(c+h)\,-\,F(c)}{h}[/itex]
[itex]m_{tangent}\,=\,\lim_{h \to 0}\,\frac{f(6\pi\,h)\,-\,F(6\pi)}{h}[/itex]
[itex]m_{tangent}\,=\,\lim_{h \to 0}\,\frac{sin(6\pi\,+\,h)}{h}[/itex]
Now use L'Hopital's Rule and take the derivative of the denominator and numerator...
[itex]\frac{d}{dh}\,\left[\frac{sin(6\pi\,+\,h)}{h}\right]\,=\,cos(h)[/itex]
[itex]y\,-\,y_1\,=\,m\,(x\,-\,x_1)[/itex]
[itex]y\,-\,(0)\,=\,(cos\,h)\,(x\,-\,6\pi)[/itex]
Since h is zero, the coefficient, m, is 1.
So your tangent line equation is then...
[itex]y\,=\,x\,-\,6\pi[/itex]