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anonymous
 one year ago
Let 'f' be differentiable at c. Let y = ax + b be the equation of the tangent line to the graph of 'f' at point [c,f(c)]. Prove that
Lim F(x)  (ax + b) = 0
x>c x  c
anonymous
 one year ago
Let 'f' be differentiable at c. Let y = ax + b be the equation of the tangent line to the graph of 'f' at point [c,f(c)]. Prove that Lim F(x)  (ax + b) = 0 x>c x  c

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dan815
 one year ago
Best ResponseYou've already chosen the best response.0whats with the xc on the bottom there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Treat that limit as a fraction i.e x c is the denominator

dan815
 one year ago
Best ResponseYou've already chosen the best response.0is f and F the same function in the question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah sorry, i must have typed it up wrong >< it's f(x)  (ax + b)

dan815
 one year ago
Best ResponseYou've already chosen the best response.0so u know this tangent line passes through the point c,f(c)

dan815
 one year ago
Best ResponseYou've already chosen the best response.0we have an indeterminate form 0/0 u can use lhopitals

dan815
 one year ago
Best ResponseYou've already chosen the best response.0or split into 2 cases, when f(x) degree <1 and f(x) degree>1

dan815
 one year ago
Best ResponseYou've already chosen the best response.0are you allowed to use L'hopitals though?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, I was about to substitute the points on the tangent into the differentiated limit to solve for: lim x>c

dan815
 one year ago
Best ResponseYou've already chosen the best response.0well here is the intuition for it

dan815
 one year ago
Best ResponseYou've already chosen the best response.0when you are very close to the c

dan815
 one year ago
Best ResponseYou've already chosen the best response.0you are travelling on your graph close to the tangent line, where as in the denomiator u are travelling horizotally towards C

dan815
 one year ago
Best ResponseYou've already chosen the best response.0so technically if u are going towards C on the tangent line itself the numerator shud be approaching 0 much faster than the denominator

dan815
 one year ago
Best ResponseYou've already chosen the best response.0eh that doesnt sound very clear lol xD forget it, if its confusing u

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah I know what you mean, I graphically picture this Thanks for the help by the way ^^

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no no, I know what's going on. It's just this particular question, I haven't gotten much practice, since I like doing the easy L'hopital questions haha

dan815
 one year ago
Best ResponseYou've already chosen the best response.0like u see the values on the graph are much closed to the tangent line as small distances away

dan815
 one year ago
Best ResponseYou've already chosen the best response.0because the smaller distances it gets the better a linear approximation is to this graph f(x)

dan815
 one year ago
Best ResponseYou've already chosen the best response.0infact it gets infintessimally better than the horizotal way of approaching on the number line

dan815
 one year ago
Best ResponseYou've already chosen the best response.0there are excepts to this way of looking at it though, for example of the graph f(x) being a horizontal line too

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0use these: \[F^/(c)=a=\lim_{x\rightarrow c }\frac{f(x)f(c)}{xc}\\\frac{yF(c)}{xc}=a\text{ which will be the equation of the tangent line..... }\]
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