# Tagged Questions

2answers
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### Indeterminate Limit (Finding the Remainder to a Root)

So i was working on this: $$\lim\limits_{x\to1} \frac{x + \sqrt{x} - 2}{x - 1}$$ and I thought to simpify my top by multiplying by a conjugate, taking everything other than the $x$ to be the $b$ ...
1answer
39 views

### $\int_0^{\infty} \lim_{m \rightarrow \infty} x_m \left( \varepsilon \right) e^{- \varepsilon} \mathrm{d} \varepsilon$

In the expression $$\int_0^{\infty} \lim_{m \rightarrow \infty} x_m \left( \varepsilon \right) e^{- \varepsilon} \mathrm{d} \varepsilon$$ Is it possible to move the integral inside the Newton's ...
3answers
69 views

### Find $\lim_{x \to \alpha}[1+ax^2+bx+c]^\frac{1}{x-\alpha}$

If $\alpha , \beta$ be the roots of $ax^2+bx+c=0$. Find $$\lim_{x \to \alpha}[1+ax^2+bx+c]^\frac{1}{x-\alpha}$$ Here $\alpha +\beta=-\frac{b}{a}$ and $\alpha \beta=\frac{c}{a}$. How can I ...
1answer
39 views

### How would you find the roots to this question?

I have a homework problem that I arrived. With Mathematica, the limit is 0. So by using $\epsilon= 10^{-6}$ (it is -6, not -0, sorry for the cutoff). $\sin(n^2)/\sqrt{n} <\epsilon =10^{-6}$ ...
3answers
1k views

### On applying the quadratic formula to a first-degree equation

You're probably thinking, "Why?" Please let me explain... It is (very) well-known that  \forall (a,b,c,x) \in \mathbb{C}^* \times \mathbb{C}^3: ax^2 + bx + c = 0 \Leftrightarrow x = \frac{-b \pm ...