Tagged Questions
1
vote
2answers
42 views
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 $b$ ...
2
votes
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 ...
0
votes
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 ...
0
votes
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).
$\sin(n^2)/\sqrt{n} <\epsilon =10^{-6}$
...
15
votes
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 ...
