Tag: functions
- $\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^{x} = e,\ $ and $\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^{x} = \frac{1}{e}.\ $ Is this generalisable
- When is the image of an entire function all of $\mathbb{C}$
- Range of $y=a\sin(x)+b\,\mathrm{cosec}(x)$ where $a$ and $b$ are real and $a,b\ne0$
- Find $f(1729)$ if $n^2\int_{x}^{x+\frac 1 n} f(t)\;\text{d}t=nf(x)+0.5$
- Finding the maximum and minimum of a multivariable function on a domain
- Showing that a function is differentiable in a point $a$ given $f’$ is uniformly continuous
- Why are zeros of functions so important
- Why is $f:{\mathbb N}\to{\mathbb N}$, f(x) = 17 neither surjective nor injective
- Expressing $f(x) = \frac{x-1}{x+1}$ as a sum of an even and odd function
- Finding number of solutions of $f(x)=f^{-1}(x)$ where $f(x)=x^3+x-1$