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anonymous

  • 5 years ago

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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  1. anonymous
    • 5 years ago
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    dont use the definition, cheat and use the quotient rule

  2. myininaya
    • 5 years ago
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    ok eric cartman

  3. anonymous
    • 5 years ago
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    lols

  4. myininaya
    • 5 years ago
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    how do i reach these kids

  5. anonymous
    • 5 years ago
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    ok you write it out myininaya lets see you write this in latex using the definition. i will wait...

  6. myininaya
    • 5 years ago
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    i cant scan it in? :(

  7. anonymous
    • 5 years ago
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    let me know when you get \[\frac{-1}{(x-6)^2}\]

  8. anonymous
    • 5 years ago
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    no you have to use latex

  9. myininaya
    • 5 years ago
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    \[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}}\frac{x-5-2(x-6)}{(x-6)(x-7)\] =\[\lim_{x \rightarrow 7}\frac{x-5-2x+12}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-x+7}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-(x-7)}{(x-6)(x-7)}\] \[\lim_{x \rightarrow 7}\frac{-1}{x-6}=\frac{-1}{7-6}=\frac{-1}{1}=-1\]

  10. anonymous
    • 5 years ago
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    i cant do it

  11. myininaya
    • 5 years ago
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    no some of got messed up :(

  12. anonymous
    • 5 years ago
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    i am totally impressed

  13. anonymous
    • 5 years ago
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    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!

  14. myininaya
    • 5 years ago
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    :)

  15. anonymous
    • 5 years ago
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    wow its gettin heated up in here

  16. myininaya
    • 5 years ago
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    i will rewrite the top

  17. anonymous
    • 5 years ago
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    myininaya is showing me up;(

  18. anonymous
    • 5 years ago
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    hahaha whose the better mathematician?

  19. myininaya
    • 5 years ago
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    \[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-6}{x-6}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-5-2(x-6)}{(x-6)(x-7)}\]

  20. myininaya
    • 5 years ago
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    satellite is way better than me

  21. anonymous
    • 5 years ago
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    haha

  22. anonymous
    • 5 years ago
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    \[lim_{h->0}\frac{\frac{x+h-5}{x+h-6}-\frac{x-5}{x-6}}{h}\]

  23. anonymous
    • 5 years ago
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    how do you like dem apples?

  24. myininaya
    • 5 years ago
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    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

  25. myininaya
    • 5 years ago
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    very cute satellite

  26. anonymous
    • 5 years ago
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    right. once you have m = -1 it is all gravy from there

  27. anonymous
    • 5 years ago
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    haha sweet already worked it out. thanks guys

  28. anonymous
    • 5 years ago
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    good!

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