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## Main Question or Discussion Point

I noticed there's a pattern to the special cases f(x)=ax+b and f(x)=x^2:

[tex]lim_{x\rightarrow c}ax+b=L, \delta=\frac{\epsilon}{a}[/tex]

[tex]lim_{x\rightarrow c}x^2=L, \delta=\frac{\epsilon}{2c+1}[/tex]

I noticed that a is the derivative of ax+b, and 2x(2c) is the derivative of x^2, but how do I justify the + 1 part of the special case for x^2?

Is there any formula for a general case?

[tex]lim_{x\rightarrow c}ax+b=L, \delta=\frac{\epsilon}{a}[/tex]

[tex]lim_{x\rightarrow c}x^2=L, \delta=\frac{\epsilon}{2c+1}[/tex]

I noticed that a is the derivative of ax+b, and 2x(2c) is the derivative of x^2, but how do I justify the + 1 part of the special case for x^2?

Is there any formula for a general case?