Consider the graph defined by http://www.webassign.net/cgi-bin/symimage.cgi?expr=y%20%3D%20%28x%20-%205%29%2F%28x%20-%206%29 (a) Use the definition of the derivative to find the slope of the tangent line to the graph at the point (7, 2). slope = (b) Find an equation of the tangent line to the graph at the point (7, 2). y =

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Consider the graph defined by http://www.webassign.net/cgi-bin/symimage.cgi?expr=y%20%3D%20%28x%20-%205%29%2F%28x%20-%206%29 (a) Use the definition of the derivative to find the slope of the tangent line to the graph at the point (7, 2). slope = (b) Find an equation of the tangent line to the graph at the point (7, 2). y =

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dont use the definition, cheat and use the quotient rule
ok eric cartman
lols

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Other answers:

how do i reach these kids
ok you write it out myininaya lets see you write this in latex using the definition. i will wait...
i cant scan it in? :(
let me know when you get \[\frac{-1}{(x-6)^2}\]
no you have to use latex
\[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}}\frac{x-5-2(x-6)}{(x-6)(x-7)\] =\[\lim_{x \rightarrow 7}\frac{x-5-2x+12}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-x+7}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-(x-7)}{(x-6)(x-7)}\] \[\lim_{x \rightarrow 7}\frac{-1}{x-6}=\frac{-1}{7-6}=\frac{-1}{1}=-1\]
i cant do it
no some of got messed up :(
i am totally impressed
on the other hand i was trying to write a compound fraction because i was just trying to find the derivative, not the value at 7. good work!
:)
wow its gettin heated up in here
i will rewrite the top
myininaya is showing me up;(
hahaha whose the better mathematician?
\[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-6}{x-6}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-5-2(x-6)}{(x-6)(x-7)}\]
satellite is way better than me
haha
\[lim_{h->0}\frac{\frac{x+h-5}{x+h-6}-\frac{x-5}{x-6}}{h}\]
how do you like dem apples?
so anyways we found the slope of the tangent line to be -1 so a tangent line has form y=mx+b just like any other line we know m=-1 we also know a point on the line (7,2) so we can find b 2=-1(7)+b 2=-7+b 2+7=b 9=b so the equation is y=-x+9
very cute satellite
right. once you have m = -1 it is all gravy from there
haha sweet already worked it out. thanks guys
good!

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