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

Question

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

dan815 · Answer

whats with the x-c on the bottom there

anonymous · Answer

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

dan815 · Answer

is f and F the same function in the question

anonymous · Answer

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

dan815 · Answer

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

dan815 · Answer

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

anonymous · Answer

okay

dan815 · Answer

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

dan815 · Answer

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