How is $\frac{10x\Delta x +5( \Delta x)^2}{\Delta x}=10x+ 5\Delta x$, and not $10x\Delta x+5\Delta x$, or $10x+5(\Delta x)^2$? What am I missing here? (Even though this may be an algebraic error, perhaps I should know why if I understood the change of x correctly?)
2026-04-22 07:25:41.1776842741
Why is $\frac{10x\Delta x +5( \Delta x)^2}{\Delta x}=10x+ 5\Delta x$? (Algebra error)
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I'm not sure what your confusion is about, but it seems that if you factor out $\Delta x$ in the numerator, you have
$$ \frac{10x\Delta x + 5 (\Delta x)^2}{\Delta x} = \frac{\Delta x(10x + 5\Delta x)}{\Delta x} = 10x + 5\Delta x $$