# Tagged Questions

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### Function Equivalent to a Constant Paradox

Say I define $z(x,y) = x^2+y = \text{constant}$ Then $\left(\dfrac{\partial z}{\partial x}\right)_{y} = 2x$ However, $\left(\dfrac{\partial \text{ constant}}{\partial x}\right)_y = 0$ Shouldn't ...
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### Clarification of Identification [on hold]

This is more of an observation question. When you see $x$, In $f(x) = x^2$ And when you see $g(x) = x^3$ You automatically identify $x = x$ Wouldn't the $x$'s be off by a little bit? But ...
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### Limit of a function containing square root.

Q. $\lim _{x\to 0}\frac{\left(\sqrt{1-cos2x}\right)}{x}$ We can write this function as $\lim _{x\to 0}\frac{\left(\sqrt{2sin^2x}\right)}{x}$. Algebraically we have ...
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### How to combine two functions into one continuous function so it can be integrated/differentiated?

I have a function like this : $$f(x)=\begin{cases}x \in)-\infty, 1)&,\;\;f(x)=x^2\\{}\\x\in(1,+\infty(&,\;\;f(x)=x^3\end{cases}\;\;\;\;\;\;$$ as you can see, the function as a whole is ...
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