# Questions tagged [indeterminate-forms]

If the expression obtained after any substitution during limit analysis does not give enough information to determine the original limit, it is known as an indeterminate form.

354 questions
Filter by
Sorted by
Tagged with
79 views

### Proof of $\lim_{n\to \infty}(1 + \frac{b}{n})^n = e^b$ [duplicate]

I found one definition of $e$ to be $\lim_{n\to \infty}(1 + \frac{1}{n})^n = e$ and I checked it with a graphing calculator to be true. However the $1$ in the numerator is a special case, where it ...
97 views

46 views

### Explaining indeterminate forms

A student of mine asked me why $+\infty -\infty$ and $\frac{\infty}{\infty}$ are considered indeterminate forms. I think that this is an only apparently stupid question. In other words how can I show, ...
How do I solve this question? Please explain if possible how the method striked you too. $$\lim _{x\to 0}\left(\frac{\sqrt{p+x}-\sqrt{p-x}}{\sqrt{q+x}-\sqrt{q-x}}\right)$$ I tried double rationalising ...