advice the limit \\displaystyle\\lim_h\\rightarrow0\\frac\\left(x-h\\right)^3-x^3h ?


You are watching: Lim h → 0 (x + h)3 − x3 h

\\displaystyle\\lim_h\\rightarrow0\\frac\\left(x-h\\right)^3-x^3h=-3x^2 Explanation:We seek: \\displaystyleL=\\lim_h\\rightarrow0\\frac\\left(x-h\\right)^3-x^3h ...
By definition \\lim_h \\to 0 \\frac(x+h)^4 -x^4h=(x^4)'=4x^3. Also, \\lim_h \\to 0 \\frac(x+h)^4 -x^4h= \\lim_h \\to 0 \\fracx^4+4x^3h+6x^2h^2+4xh^3+h^4 -x^4h=4x^3
https://math.stackexchange.com/questions/2942204/prove-by-the-limit-definition-that-lim-x-rightarrow-2-fracx2-1x-3-3
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