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

[luke00628063]

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.

 

[anuttarasammyak]

In my sense, $\triangle x \rightarrow dx$ in introducing integral or derivative. I feel some background information is missing in your question.

 

[WWGD]

$\Delta y:= y(x+h)-y(x)$, 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.

 

[PeroK]

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.

 

[WWGD]

$dx$ 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.

 

[pasmith]

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.