Exam asks me for a case where ▲x > dx?

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I'm studying for an exam and I was checking old exams so I could practice, and I found this question that make me feel like I don't know anything:
"Explain in which cases ▲x > dx and give a graphical example."
I have always been taught derivatives with the typical graph with the tangent and the secant lines where the difference between ▲y and dy is obvious and delta x and dx are equals but never one example where ▲x != dx or in this case, ▲x > dx. Am I missing something? Just in case, I'm in the first year of system engineering.
 
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In my sense, ##\triangle x \rightarrow dx## in introducing integral or derivative. I feel some background information is missing in your question.
 
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##\Delta y:= y(x+h)-y(x)##, while ##dy## is the change along the linear approximation by a hyperplane ; a ( tangent) line when you use a single variable. The linear approximation is given by ##f'(x)dx##. Try finding an example.
 
luke00628063 said:
I'm studying for an exam and I was checking old exams so I could practice, and I found this question that make me feel like I don't know anything:
"Explain in which cases ▲x > dx and give a graphical example."
I have always been taught derivatives with the typical graph with the tangent and the secant lines where the difference between ▲y and dy is obvious and delta x and dx are equals but never one example where ▲x != dx or in this case, ▲x > dx. Am I missing something? Just in case, I'm in the first year of system engineering.
##dx## is not a number, so I would say the question makes no sense.
 
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##dx## in here takes the value ##h##, as in ##lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{(x+h)-x}##, so it is a variable, but takes numerical values.
 
luke00628063 said:
I'm studying for an exam and I was checking old exams so I could practice, and I found this question that make me feel like I don't know anything:
"Explain in which cases ▲x > dx and give a graphical example."
I have always been taught derivatives with the typical graph with the tangent and the secant lines where the difference between ▲y and dy is obvious and delta x and dx are equals but never one example where ▲x != dx or in this case, ▲x > dx. Am I missing something? Just in case, I'm in the first year of system engineering.

Are you sure x is the independent variable here? Perhaps x is a function of time, making it like y in your example.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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