Finding Limits with DeltaX: An Essential Tool for Calculus

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To eliminate the last delta x in calculus problems, one should take the limit as delta x approaches zero. It is essential to maintain the limit notation, lim(Δx → 0), in every step of the calculation until the limit is fully evaluated. This approach ensures that the process adheres to the principles of calculus. Properly applying limits is crucial for achieving accurate results in derivative and integral calculations. Understanding this concept is fundamental for mastering calculus techniques.
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Homework Statement
Lim as F(x)= (x+δx)^2-2(x+δx)+1(x^2-2x+1)/δx
δx-> 0

I have a δx left over and i don’t know how to get rid of it.
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Lim as F(x)= (x+δx)^2-2(x+δx)+1(x^2-2x+1)/δx
δx-> 0
How can i get rid of the last delta x
 

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Witcher said:
I have a δx left over and i don’t know how to get rid of it.
How can i get rid of the last delta x

Take the limit as ##\delta x \rightarrow 0##.
 
like this right
 

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Witcher said:
like this right

The idea is correct. I would say you need to keep ##\lim_{\Delta x \rightarrow 0}## in every line until you take the limit.
 
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