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whats with the x-c on the bottom there

Treat that limit as a fraction
i.e x -c is the denominator

is f and F the same function in the question

Ah sorry, i must have typed it up wrong ><
it's f(x) - (ax + b)

so u know this tangent line passes through the point c,f(c)

we have an indeterminate form 0/0 u can use lhopitals

okay

or split into 2 cases, when f(x) degree <1 and f(x) degree>1

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Ah okay

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are you allowed to use L'hopitals though?

yeah absolutely

ah i see

well here is the intuition for it

when you are very close to the c

eh that doesnt sound very clear lol xD forget it, if its confusing u

yeah I know what you mean, I graphically picture this
Thanks for the help by the way ^^

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like u see the values on the graph are much closed to the tangent line as small distances away

closer*

at small distances

because the smaller distances it gets the better a linear approximation is to this graph f(x)

infact it gets infintessimally better than the horizotal way of approaching on the number line

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k well cheers