# Finding the slope using limits

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Thread starter 3 months ago
#1
I managed to find the answer using uv'-vu'/v^2 but I wanna know how we can find the answer using limits with something like f(x+h)-f(x)/h
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3 months ago
#2
(Original post by cj104)
I managed to find the answer using uv'-vu'/v^2 but I wanna know how we can find the answer using limits with something like f(x+h)-f(x)/h

It is now useful to use Binomial theorem on in increasing powers of since is small when it tends to zero.

EDIT: Even better, just multiply numerator and denominator by , simplify to get rid of the singularity at h=0, and get the limit by subbing in h=0.
Last edited by RDKGames; 3 months ago
0
3 months ago
#3
(Original post by RDKGames)
EDIT: Even better, just multiply numerator and denominator by , simplify to get rid of the singularity at h=0, and get the limit by subbing in h=0.
Not only is this simpler, but it avoids the circularity that proofs of the binomial theorem usually assume you've already proved is differentiable.
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